All Algebra 1 Resources
Example Questions
Example Question #91 : Perpendicular Lines
Suppose a line has an x-intercept of one and a y-intercept of two. What is the equation of the perpendicular line which pass through the point ?
Write the points that correspond to the x and y-intercepts given in the problem.
X-intercept of one:
Y-intercept of two:
Find the slope of this line connected with these points.
The slope is negative two. The slope of the perpendicular line is the negative reciprocal of this slope.
Write the slope-intercept form.
Substitute the perpendicular slope with the point that this line will pass through.
Solve for the y-intercept, .
Subtract nine halves on both sides.
Simplify both sides.
With the perpendicular slope and the y-intercept, write the equation of the line.
The answer is:
Example Question #331 : Functions And Lines
What is the slope of a line perpendicular to the line with the following equation?
Answer cannot be determined from this information.
Step 1: get the line into y = mx +b format to find the slope m:
Next, we need to remember that perpendicular lines have slopes that are negative reciprocals. Find the negative reciprocal of :
Example Question #1 : How To Find The Equation Of A Line
Given two points, (5, –8) (–2, 6), what is the equation of the line containing them both?
y = (2/7)x – 8
y = 2x – 2
y = –2x + 2
y = (–2/7)x + 8
No Solution
y = –2x + 2
First, you should plug the given points, (5, –8) (–2, 6), into the slope formula to find the slope of the line.
Then, plug the slope into the slope formula, y = mx + b, where m is the slope.
y = –2x + b
Plug in either one of the given points, (5, –8) or (–2, 6), into the equation to find the y-intercept (b).
6 = –2(–2) + b
6 = 4 + b
2 = b
Plug in both the slope and the y-intercept into slope intercept form.
y = –2x + 2
Example Question #1 : How To Find The Equation Of A Line
What is the equation of a line with slope of 3 and a y-intercept of –5?
y = –5x + 3
y = 3x + 5
y = 5x – 3
y = 3x – 5
y = (3/5)x + 2
y = 3x – 5
These lines are written in the form y = mx + b, where m is the slope and b is the y-intercept. We know from the question that our slope is 3 and our y-intercept is –5, so plugging these values in we get the equation of our line to be y = 3x – 5.
m = 3 and b = –5
Example Question #1 : How To Find The Equation Of A Line
A line contains the points (8, 3) and (-4, 9). What is the equation of the line?
is the slope-intercept form of the equation of a line.
Slope is equal to between points, or .
So .
At point (8, 3 ) the equation becomes
So
Example Question #2 : How To Find The Equation Of A Line
Given two points and , find the equation of a line that passes through the point and is parallel to the line passing through points and .
The slope of the line passing through points and can be computed as follows:
Now, the new line, since it is parallel, will have the same slope. To find the equation of this new line, we use point-slope form:
, where is the slope and is the point the line passes through.
After rearranging, this becomes
Example Question #1 : How To Find The Equation Of A Line
Find the equation, in form, of the line that contains the points and .
When finding the equation of a line from some of its points, it's easiest to first find the line's slope, or .
To find slope, divide the difference in values by the difference in values. This gives us divided by , or .
Next, we just need to find , which is the line's -intercept. By plugging one of the points into the equation , we obtain a value of 11 and a final equation of
Example Question #4 : How To Find The Equation Of A Line
We can find the equation of th line in slope-intercept form by finding and .
First, calculate the slope, , for any two points. We will use the first two.
Next, using the slope and any point on the line, calculate the y-intercept, . We will use the first point.
The correct equation in slope-intercept form is .
Example Question #3 : How To Find The Equation Of A Line
What is the equation of a line with a slope of and a -intercept of ?
None of the above
When a line is in the format, the is its slope and the is its -intercept. In this case, the equation with a slope of and a -intercept of is .
Example Question #1 : How To Find The Equation Of A Line
In 1990, the value of a share of stock in General Vortex was $27.17. In 2000, the value was $48.93. If the value of the stock rose at a generally linear rate between those two years, which of the following equations most closely models the price of the stock, , as a function of the year, ?
We can treat the price of the stock as the value and the year as the value, making any points take the form , or . This question is asking for the line that includes points and .
To find the equation, first, we need the slope.
Now use the point-slope formula with this slope and either point (we will choose the second).