How to Write Lines in Slope Intercept Form

The slope intercept form is probably the most frequently used way  to express equation of a line. To be able to use slope intercept form, all that you need to be able to do is 1) find the slope of a line and 2) find the y-intercept of a line.

Video Tutorial on Slope Intercept Form

The Formula

In general, the slope intercept form assumes the formula: y = mx + b.

• M is the slope (lesson on slope)
  • Mnemonic : 'm' means 'move'
• B is the y-intercept (lesson on the y-intercept)
  • Mnemonic: 'b' means where the line begins.

Examples

• y = 5x + 3 is an example of the Slope Intercept Form and represents the equation of a line with a slope of 5 and and a y-intercept of 3.
• y = −2x + 6 represents the equation of a line with a slope of −2 and and a y-intercept of 6.

Vertical and Horizontal lines

Vertical Lines

The Equation of a vertical line is x = b.

Since a vertical line goes straight up and down, its slope is undefined. Also, the x value of every point on a vertical line is the same. Therefore, whatever the x value is, is also the value of 'b'.

For instance, the red line in the picture below is the graph of the x = 1.

Horizontal Lines

The equation of a horizontal line is y = b where b is the y-intercept.

Since the slope of a horizontal line is 0, the general formula for the standard form equation, y = mx + b becomes y = 0x + b y = b. Also,since the line is horizontal, every point on that line has the exact same y value. This y-value is therefore also the y-intercept. For instance, the red line in the picture below is the graph of the horizontal line y = 1. (In depth lesson on the equation of a horizontal line)

Practice Problems

Problem 1

Problem 2

Look at the picture of the graph below. Find the slope of this line, its y-intercept, then express the equation of this line in slope intercept form.

What is the slope of the line ?

Step 1

What is the y-intercept of the line?

slope = $$ \frac{rise}{run} = \frac{-2}{1} = -2 $$

Step 2

What is the slope intercept form of this line?

-1 which is the y coordinate of the point (0, -1).

Step 3

What is the slope intercept form of the line pictured in the graph below?

The general formula is y = mx + b.

m = slope = -2
b = y-intercept of the line = -1

Therefore, the slope intercept form of this line is y = -2x - 1.

Problem 3

What is the slope intercept form of the line pictured in the graph below?

Problem 4

What is the slope intercept form of the line pictured in the graph below?

Practice Problems

Write the slope intercept form for the lines below.

Problem 5

In the general form:
y = mx + b
m = slope = 2
b = the y intercept = 12

The slope intercept form of the equation:
y = 2x + 12

Problem 6

In the general form:
y = mx + b
m = slope = 3
b = the y-intercept = -5

The slope intercept form of the equation:
y = 3x - 5

Problem 7

In the general form:
y = mx + b
m = slope = ½
b = the y intercept = 7

The slope intercept form of the equation:
y = ½x + 7

How to Write Lines in Slope Intercept Form

Source: https://www.mathwarehouse.com/algebra/linear_equation/slope-intercept-form.php

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