﻿ Equation of a line Given slope and A point. Video tutorial and practice problems . It's easy to ...

# Equation of a Line Given Slope and a Point

How to write the equation

How to write equation of a line, given the slope of a line and also one of points on the line.

Students are often asked to find the equation of a line that passes through a point and has a certain slope.. Watch the video tutorial below to understand how to do these problems and, if you want, download this free worksheet if you want some extra practice.

### Video Tutorial on Equation from Slope and a Point

Steps to follow:
Example: How to find the equation of a line that goes through the point (1, 3) and has a slope of 2.
What we know from the problem: that the slope is 2 so we can write y = 2x + b
Our goal: to find the y-intercept or "b"

Step 1

Substitute slope for 'm' in y = mx + b
y = mx +b
y = 2x + b

Step 2

Substitute the point (1,3) into equation
y = 2x + b
3 = 2(1) +b

Step 3

Solve for b
3 = 2+b
3-2 = 1= b

Step 4

Now that we know b, all that we have to do is put it into the equation and we now have our line in slope intercept form
y = 2x+1

Below is a picture of y = 2x + 1

### Practice Problems

Try to write (or mentally make a note) of each equation below.

Goal

Find "b", the y-intercept

y = ½x + b

Step 1

Substitute in the point (2,3)

3 = ½(2)+ b

Step 2

Solve equation for b

3 = 1 + b
3 - 1 = 2 = b

Last Step

Insert b into equation

y = ½x +2

Below is graph of y = ½x +2

Step 1

Plug slope into M

y = 10x + b

Step 2

Substitute x and y coordinates of point

34 = 10 •3 + b 28 = 30 + b

Step 3

Solve equation for B

34 - 30 = b
4 = b

Step 4

Plug in B as the y-intercept and write standard form equation.

y = 10x + 4

Step 1

Plug slope into M

y = 3x + b

Step 2

Substitute x and y coordinates of point

23 = 3 × 6 +b 23 = 18 + b

Step 3

Solve equation for B

23 - 18 = b = 5

Step 4

Plug in B as the y-intercept and write standard form equation.

y = 3x + 5

There are two ways to approach this problem. First, you can look at this as a horizontal line, any horizontal line has the standard form equation of y = b where b is the y intercept. Since the slope is 0, and only horizontal lines have a slope of zero, all points on this line including the y-intercept must have the same y value. This y-value is 5, which we can get from the fact that the line passes through the point (7,5). Therefore the standard form equation of this horizontal line is y = 5.

Step 1

Plug slope into M

y = 0x + b

Step 2

Substitute x and y coordinates of point

5 = 0 • 7 + b 5 = b

Step 3

Solve equation for B

b = 5

Step 4

Plug in B as the y-intercept and write standard form equation.

y = 0x + 5 y = 5

Since the slope is undefined, the line is a vertical line. Therefore, the equation is just x = -3.

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