# GMAT Math : Calculating the equation of a line

## Example Questions

### Example Question #1 : Calculating The Equation Of A Line

What is the equation of a line with slope  and a point ?

Explanation:

Since the slope and a point on the line are given, we can use the point-slope formula:

### Example Question #2 : Calculating The Equation Of A Line

What is the equation of a line with slope  and point ?

Explanation:

Since the slope and a point on the line are given, we can use the point-slope formula:

### Example Question #3 : Calculating The Equation Of A Line

What is the equation of a line with slope  and a point ?

Explanation:

Since the slope and a point on the line are given, we can use the point-slope formula:

slope: and point:

### Example Question #1 : Other Lines

Find the equation of the line through the points  and .

Explanation:

First find the slope of the equation.

Now plug in one of the two points to form an equation.  Here we use (4, -2), but either point will produce the same answer.

### Example Question #5 : Calculating The Equation Of A Line

Consider segment  which passes through the points  and .

Find the equation of  in the form .

Explanation:

Given that JK passes through (4,5) and (144,75) we can find the slope as follows:

Slope is found via:

Plug in and calculate:

Next, we need to use one of our points and the slope to find our y-intercept. I'll use (4,5).

### Example Question #6 : Calculating The Equation Of A Line

Determine the equation of a line that has the points  and  ?

Explanation:

The equation for a line in standard form is written as follows:

Where  is the slope and  is the y intercept. We start by calculating the slope between the two given points using the following formula:

Now we can plug either of the given points into the formula for a line with the calculated slope and solve for the y intercept:

We now have the slope and the y intercept of the line, which is all we need to write its equation in standard form:

### Example Question #7 : Calculating The Equation Of A Line

Give the equation of the line that passes through the -intercept and the vertex of the parabola of the equation

.

Explanation:

The -intercept of the parabola of the equation can be found by substituting 0 for :

This point is .

The vertex of the parabola of the equation  has -coordinate , and its -coordinate can be found using substitution for . Setting  and :

The vertex is

The line connects the points  and . Its slope is

Since the line has -intercept  and slope , the equation of the line is , or .

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