How to find the equation of a line - SSAT Upper Level Quantitative
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Given the graph of the line below, find the equation of the line.
Given the graph of the line below, find the equation of the line.
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To solve this question, you could use two points such as (1.2,0) and (0,-4) to calculate the slope which is 10/3 and then read the y-intercept off the graph, which is -4.
To solve this question, you could use two points such as (1.2,0) and (0,-4) to calculate the slope which is 10/3 and then read the y-intercept off the graph, which is -4.
Give the equation of the line through 
and 
.
Give the equation of the line through
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First, find the slope:
Apply the point-slope formula:
Rewriting in standard form:
First, find the slope:
Apply the point-slope formula:
Rewriting in standard form:
A line can be represented by 
. What is the slope of the line that is perpendicular to it?
A line can be represented by
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You will first solve for Y, to get the equation in 
form.
represents the slope of the line, which would be 
.
A perpendicular line's slope would be the negative reciprocal of that value, which is 
.
You will first solve for Y, to get the equation in
A perpendicular line's slope would be the negative reciprocal of that value, which is
Examine the above diagram. What is 
?
Examine the above diagram. What is
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Use the properties of angle addition:
Use the properties of angle addition:
Give the equation of a line that passes through the point 
and has an undefined slope.
Give the equation of a line that passes through the point
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A line with an undefined slope has equation 
for some number 
; since this line passes through a point with 
-coordinate 4, then this line must have equation 
A line with an undefined slope has equation
Give the equation of a line that passes through the point 
and has slope 1.
Give the equation of a line that passes through the point
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We can use the point slope form of a line, substituting 
.
or
We can use the point slope form of a line, substituting
or
Find the equation the line goes through the points 
and 
.
Find the equation the line goes through the points
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First, find the slope of the line.
Now, because the problem tells us that the line goes through 
, our y-intercept must be 
.
Putting the pieces together, we get the following equation:
First, find the slope of the line.
Now, because the problem tells us that the line goes through
Putting the pieces together, we get the following equation:
A line passes through the points 
and 
. Find the equation of this line.
A line passes through the points
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To find the equation of a line, we need to first find the slope.
Now, our equation for the line looks like the following:
To find the y-intercept, plug in one of the given points and solve for 
. Using 
, we get the following equation:
Solve for 
.
Now, plug the value for 
into the equation.
To find the equation of a line, we need to first find the slope.
Now, our equation for the line looks like the following:
To find the y-intercept, plug in one of the given points and solve for
Solve for
Now, plug the value for
What is the equation of a line that passes through the points 
and 
?
What is the equation of a line that passes through the points
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First, we need to find the slope of the line.
Next, find the 
-intercept. To find the 
-intercept, plug in the values of one point into the equation 
, where 
is the slope that we just found and 
is the 
-intercept.
Solve for 
.
Now, put the slope and 
-intercept together to get 
First, we need to find the slope of the line.
Next, find the
Solve for
Now, put the slope and
Are the following two equations parallel?
Are the following two equations parallel?
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When two lines are parallal, they must have the same slope.
Look at the equations when they are in slope-intercept form, 
where b represents the slope.
We must first reduce the second equation since all of the constants are divisible by 
.
This leaves us with 
. Since both equations have a slope of 
, they are parallel.
When two lines are parallal, they must have the same slope.
Look at the equations when they are in slope-intercept form,
We must first reduce the second equation since all of the constants are divisible by
This leaves us with
Reduce the following expression:
Reduce the following expression:
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For this expression, you must take each variable and deal with them separately.
First divide you two constants 
.
Then you move onto 
and when you divide like exponents you must subtract the exponents leaving you with 
.
is left by itself since it is already in a natural position.
Whenever you have a negative exponential term, you must it in the denominator.
This leaves the expression of 
.
For this expression, you must take each variable and deal with them separately.
First divide you two constants
Then you move onto
Whenever you have a negative exponential term, you must it in the denominator.
This leaves the expression of
A line is defined by the following equation:
What is the slope of that line?
A line is defined by the following equation:
What is the slope of that line?
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The equation of a line is
y=mx + b where m is the slope
Rearrange the equation to match this:
7x + 28y = 84
28y = -7x + 84
y = -(7/28)x + 84/28
y = -(1/4)x + 3
m = -1/4
The equation of a line is
y=mx + b where m is the slope
Rearrange the equation to match this:
7x + 28y = 84
28y = -7x + 84
y = -(7/28)x + 84/28
y = -(1/4)x + 3
m = -1/4
If the coordinates (3, 14) and (_–_5, 15) are on the same line, what is the equation of the line?
If the coordinates (3, 14) and (_–_5, 15) are on the same line, what is the equation of the line?
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First solve for the slope of the line, m using y=mx+b
m = (y2 – y1) / (x2 – x1)
= (15 – 14) / (_–_5 _–_3)
= (1 )/( _–_8)
=_–_1/8
y = –(1/8)x + b
Now, choose one of the coordinates and solve for b:
14 = –(1/8)3 + b
14 = _–_3/8 + b
b = 14 + (3/8)
b = 14.375
y = –(1/8)x + 14.375
First solve for the slope of the line, m using y=mx+b
m = (y2 – y1) / (x2 – x1)
= (15 – 14) / (_–_5 _–_3)
= (1 )/( _–_8)
=_–_1/8
y = –(1/8)x + b
Now, choose one of the coordinates and solve for b:
14 = –(1/8)3 + b
14 = _–_3/8 + b
b = 14 + (3/8)
b = 14.375
y = –(1/8)x + 14.375
Which line passes through the points (0, 6) and (4, 0)?
Which line passes through the points (0, 6) and (4, 0)?
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P1 (0, 6) and P2 (4, 0)
First, calculate the slope: m = rise ÷ run = (y2 – y1)/(x2 – x1), so m = –3/2
Second, plug the slope and one point into the slope-intercept formula:
y = mx + b, so 0 = –3/2(4) + b and b = 6
Thus, y = –3/2x + 6
P1 (0, 6) and P2 (4, 0)
First, calculate the slope: m = rise ÷ run = (y2 – y1)/(x2 – x1), so m = –3/2
Second, plug the slope and one point into the slope-intercept formula:
y = mx + b, so 0 = –3/2(4) + b and b = 6
Thus, y = –3/2x + 6
What line goes through the points (1, 3) and (3, 6)?
What line goes through the points (1, 3) and (3, 6)?
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If P1(1, 3) and P2(3, 6), then calculate the slope by m = rise/run = (y2 – y1)/(x2 – x1) = 3/2
Use the slope and one point to calculate the intercept using y = mx + b
Then convert the slope-intercept form into standard form.
If P1(1, 3) and P2(3, 6), then calculate the slope by m = rise/run = (y2 – y1)/(x2 – x1) = 3/2
Use the slope and one point to calculate the intercept using y = mx + b
Then convert the slope-intercept form into standard form.
Let y = 3_x_ – 6.
At what point does the line above intersect the following:
Let y = 3_x_ – 6.
At what point does the line above intersect the following:
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If we rearrange the second equation it is the same as the first equation. They are the same line.
If we rearrange the second equation it is the same as the first equation. They are the same line.
What is the equation of a line that passes through coordinates (2,6) and (3,5)?
What is the equation of a line that passes through coordinates (2,6) and (3,5)?
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Our first step will be to determing the slope of the line that connects the given points.
Our slope will be 
. Using slope-intercept form, our equation will be 
. Use one of the give points in this equation to solve for the y-intercept. We will use (2,6).
Now that we know the y-intercept, we can plug it back into the slope-intercept formula with the slope that we found earlier.
This is our final answer.
Our first step will be to determing the slope of the line that connects the given points.
Our slope will be
Now that we know the y-intercept, we can plug it back into the slope-intercept formula with the slope that we found earlier.
This is our final answer.
What is the slope-intercept form of 8x-2y-12=0?
What is the slope-intercept form of 8x-2y-12=0?
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The slope intercept form states that y=mx+b. In order to convert the equation to the slope intercept form, isolate y on the left side:
8x-2y=12
-2y=-8x+12
y=4x-6
The slope intercept form states that y=mx+b. In order to convert the equation to the slope intercept form, isolate y on the left side:
8x-2y=12
-2y=-8x+12
y=4x-6
Which of the following equations does NOT represent a line?
Which of the following equations does NOT represent a line?
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The answer is 
.
A line can only be represented in the form 
or 
, for appropriate constants 
, 
, and 
. A graph must have an equation that can be put into one of these forms to be a line.
represents a parabola, not a line. Lines will never contain an 
term.
The answer is
A line can only be represented in the form
A line has a slope of 
and passes through the point 
. Find the equation of the line.
A line has a slope of
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In finding the equation of the line given its slope and a point through which it passes, we can use the slope-intercept form of the equation of a line:
, where 
is the slope of the line and 
is its 
-intercept.
Plug the given conditions into the equation to find the 
-intercept.
Multiply:
Subtract 
from each side of the equation:
Now that you have solved for 
, you can write out the full equation of the line:
In finding the equation of the line given its slope and a point through which it passes, we can use the slope-intercept form of the equation of a line:
Plug the given conditions into the equation to find the
Multiply:
Subtract
Now that you have solved for