Algebra - SSAT Upper Level Quantitative

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.

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

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

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

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 we rearrange the second equation it is the same as the first equation. They are the same line.

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 .

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.

The slope intercept form states that . In order to convert the equation to the slope intercept form, isolate on the left side:

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.

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:

, where is the slope of the line and is its -intercept.

Since the problem gives us the slope of the line , we just need to use the point that is given to us to find the -intercept. Plug in known values for and taken from the given point into the equation to find the -intercept:

Multiply:

Subtract from each side of the equation:

Now that you've solved for , you can plug the given slope and the -intercept into the slope-intercept form of the equation of a line to figure out the answer:

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.

Since the problem gives us the slope of the line , we just need to use the point that is given to us to find the -intercept. Plug in known values for and taken from the given point into the equation and solve for to find the -intercept:

Multiply:

Subtract from both sides of the equation:

Now, we can write the final equation by plugging in the given slope and the -intercept :

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.

Since the problem gives us the slope of the line , we just need to use the point that is given to us to find the -intercept. Plug in known values for and taken from the given point into the equation and solve for to find the -intercept:

Multiply:

Add to each side of the equation:

Now, we can write the final equation by plugging in the given slope and the -intercept :

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.

Since the problem gives us the slope of the line , we just need to use the point that is given to us to find the -intercept. Plug in known values for and taken from the given point into the equation and solve for to find the -intercept:

Multiply:

Subtract from each side of the equation:

Now, we can write the final equation by plugging in the given slope and the -intercept :

The question gives us both the slope and the -intercept of the line. Remember that represents the slope, and represents the -intercept to write the following equation:

Alternatively, if you did not realize that the problem gives you the -intercept, you could solve it by using the slope-intercept form of the equation of a line:

, where is the slope of the line and is its -intercept.

Since the problem gives us the slope of the line , we would just need to use the point that is given to us to find the -intercept. We could plug in the known values for and taken from the given point into the equation and solve for to find the -intercept:

Multiplying leaves us with:

.

We could then substitute in the given slope and the -intercept into the equation to arrive at the correct answer:

The question gives us both the slope and the -intercept of the line, allowing us to write the following equation by inserting those values into the slope-intercept form of the equation of a line, :

Alternatively, if you did not realize that the problem gives you the -intercept, you could solve it by using the slope-intercept form of the equation of a line. Since the problem gives us the slope of the line , we would just need to use the point that is given to us to find the -intercept. We could plug in the known values for and taken from the given point into the equation and solve for to find the -intercept:

Multiplying leaves us with:

We could then substitute in the given slope and the -intercept into the equation to arrive at the correct answer:

First, notice that our -intercept for this line is ; we can tell this because one of the points, , is on the -axis since it has a value of for .

Now, we need to find the slope of the line. We can do that by using the slope equation:

We can substitute in the values of the provided points—,, and —and then solve for the slope of the line that connects them:

Now, put the two pieces of information together and substitute them into the equation to solve the problem:

First, notice that our -intercept for this line is ; we can tell this because one of the points, , is on the -axis since it has a value of for .

Now, we need to find the slope of the line. We can do that by using the slope equation:

We can substitute in the values of the provided points—,, and —and then solve for the slope of the line that connects them:

Now, put the two pieces of information together and substitute them into the equation to solve the problem:

First, notice that our -intercept for this line is ; we can tell this because one of the points, , is on the -axis since it has a value of for .

Now, we need to find the slope of the line. We can do that by using the slope equation:

We can substitute in the values of the provided points—,, and —and then solve for the slope of the line that connects them:

Now, put the two pieces of information together and substitute them into the equation to solve the problem:

First, notice that our -intercept for this line is ; we can tell this because one of the points, , is on the -axis since it has a value of for .

Now, we need to find the slope of the line. We can do that by using the slope equation:

We can substitute in the values of the provided points—,, and —and then solve for the slope of the line that connects them:

Now, put the two pieces of information together and substitute them into the equation to solve the problem: