Slope Intercept Form

Slope Intercept Form – Rules With Examples

Concept

Write the slope-intercept equation of the line given either the slope and y-intercept.

Rules

1. In an equation in y = mx + b, m stands for the slope and b stands for the y-intercept.
2. Substitute the slope and the y-intercept in the equation y = mx + b to write the equation.

Example

Write the slope-intercept equation of the line that has a y-intercept of -7 and a slope of $\fn_phv {\color{Teal} \frac{2}{3}}$ .

Solution

For a linear equation in the form y = mx + b, m stands for the slope and b stands for the y-intercept. Substituting in the information given in the problem, the slope (m) is $\fn_phv \frac{2}{3}$ and the y-intercept (b) is -7, so the equation becomes.
$\fn_phv {\color{Red} y=\frac{2}{3}x-7}$

Practice Slope Intercept Form

Practice Problem 1

What is the slope and y-intercept of the given equation?
y = -4x + 1

Practice Problem 2

Find an equation in slope-intercept form for a line with slope 12 and y-intercept -2.

Practice Problem 3

You want to rent a car for a few days. The initial rental fee is $20. For each day you rent the car, it is an extra charge of $5 a day. The total rental fee is determined by y = 5x + 20.
Graph the equation, and then interpret the slope and the y-intercept.

Practice Problem 4

When boarding a flight, you have to pay for the cost of your ticket and for each bag you check in. The total cost of your flight, y in dollars, can be determined by the equation y = 15x + 200, where x is the number of bags you check-in.
Drag the labels to complete the sentences.