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"

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

y = mx +b

y = 2x + b

Substitute the point (1,3) into equation

y = 2x + b

3 = 2(1) +b

Solve for b

3 = 2+b

3-2 = 1= b

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.

Find "b", the y-intercept

y = ½x + b

Substitute in the point (2,3)

3 = ½(2)+ b

Solve equation for b

3 = 1 + b

3 - 1 = 2 = b

Insert b into equation

y = ½x +2

Below is graph of y = ½x +2

Plug slope into M

y = 10x + b

Substitute x and y coordinates of point

34 = 10 •3 + b 28 = 30 + b

Solve equation for B

34 - 30 = b

4 = b

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

y = 10x + 4

Plug slope into M

y = 3x + b

Substitute x and y coordinates of point

23 = 3 × 6 +b 23 = 18 + b

Solve equation for B

23 - 18 = b = 5

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 1Plug slope into M

y = 0x + b

Substitute x and y coordinates of point

5 = 0 • 7 + b 5 = b

Solve equation for B

b = 5

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.