# SSAT Upper Level Math : Coordinate Geometry

## Example Questions

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### Example Question #1 : Lines

Given the graph of the line below, find the equation of the line.      Explanation:

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.

### Example Question #2 : How To Find The Equation Of A Line

Which line passes through the points (0, 6) and (4, 0)?

y = 2/3 + 5

y = –3/2 – 3

y = 1/5x + 3

y = 2/3x –6

y = –3/2x + 6

y = –3/2x + 6

Explanation:

P1 (0, 6) and P2 (4, 0)

First, calculate the slope:  m = rise ÷ run = (y2 – y1)/(x– 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

### Example Question #3 : Lines

What line goes through the points (1, 3) and (3, 6)?

–2x + 2y = 3

–3x + 2y = 3

3x + 5y = 2

2x – 3y = 5

4x – 5y = 4

–3x + 2y = 3

Explanation:

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.

### Example Question #4 : Lines

What is the slope-intercept form of ?      Explanation:

The slope intercept form states that . In order to convert the equation to the slope intercept form, isolate on the left side:   ### Example Question #5 : Lines

A line is defined by the following equation: What is the slope of that line?      Explanation:

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

### Example Question #11 : How To Find The Equation Of A Line

If the coordinates (3, 14) and (5, 15) are on the same line, what is the equation of the line?      Explanation:

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

### Example Question #2 : How To Find The Equation Of A Line

What is the equation of a line that passes through coordinates and ?      Explanation:

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.  ### Example Question #12 : How To Find The Equation Of A Line

Which of the following equations does NOT represent a line?      Explanation:

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.

### Example Question #14 : How To Find The Equation Of A Line

Let y = 3x – 6.

At what point does the line above intersect the following: They do not intersect

They intersect at all points

(–5,6)

(–3,–3)

(0,–1)

They intersect at all points

Explanation:

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

### Example Question #6 : Lines

A line has a slope of and passes through the point . Find the equation of the line.     Explanation:

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: ← Previous 1 3 4 5 6 7 8 9 36 37 