# PSAT Math : How to find the equation of a line

## Example Questions

2 Next →

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

Explanation:

Equation of line: ,    = slope,  = -intercept

Step 1) Find slope ():  rise/run

Step 2) Find -intercept ():

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

Whast line goes through the points  and ?

Explanation:

Let and

The slope is geven by:    so

Then we use the slope-intercept form of an equation;   so

And we convert

to standard form.

### Example Question #21 : Psat Mathematics

What is the equation of the line that passes through the points (4,7) and (8,10)?

Explanation:

In order to find the equation of the line, we will first need to find the slope between the two points through which it passes. The slope, , of a line that passes through the points and is given by the formula below:

We are given our two points, (4,7) and (8,10), allowing us to calculate the slope.

Next, we can use point slope form to find the equation of a line with this slope that passes through one of the given points. We will use (4,7).

Multiply both sides by four to eliminate the fraction, and simplify by distribution.

Subtract from both sides and add twelve to both sides.

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

Which line contains the following ordered pairs:

and

Explanation:

First, solve for slope.

Then, substitute one of the points into the equation y=mx+b.

This leaves us with the equation

### Example Question #15 : How To Find The Equation Of A Line

Refer to the above red line. What is its equation in standard form?

Explanation:

First, we need to find the slope of the above line.

The slope of a line. given two points  can be calculated using the slope formula

Set :

Second, we note that the -intercept is the point .

Therefore, in the slope-intercept form of a line, we can set  and :

Since we are looking for standard form - that is,  - we do the following:

or

### Example Question #16 : How To Find The Equation Of A Line

Refer to the above red line. What is its equation in slope-intercept form?

Explanation:

First, we need to find the slope of the above line.

The slope of a line. given two points  can be calculated using the slope formula

Set :

Second, we note that the -intercept is the point .

Therefore, in the slope-intercept form of a line, we can set  and :

### Example Question #17 : How To Find The Equation Of A Line

Refer to the above red line. A line is drawn perpendicular to that line, and with the same -intercept. What is the equation of that line in slope-intercept form?

Explanation:

First, we need to find the slope of the above line.

The slope of a line. given two points  can be calculated using the slope formula

Set :

The slope of a line perpendicular to it has as its slope the opposite of the reciprocal of 3, which is .

Since we want the line to have the same -intercept as the above line, which is the point , we can use the slope-intercept form to help us.  We set

, and solve for  in:

Substitute for  and  in the slope-intercept form, and the equation is

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

Find the equation of the line shown in the graph below:

y = x/2 + 4

y = -1/2x - 4

y = -1/2x + 4

y = 2x + 4

y = x/2 + 4

Explanation:

Based on the graph the y-intercept is 4. So we can eliminate choice y = x/2 - 4.

The graph is rising to the right which means our slope is positive, so we can eliminate choice y = -1/2x + 4.

Based on the line, if we start at (0,4) and go up 1 then 2 to the right we will be back on the line, meaning we have a slope of  (1/2).

Using the slope intercept formula we can plug in y= (1/2)x + 4.

2 Next →