Section 6-2: Slope-Intercept Form of a Linear EquationSPI 22C: select the graph that represents a given linear function expressed in

slope-intercept form

Objective: Graph and write linear equations using slope-intercept form

1. Slope-Intercept form: y = mx + b2. Standard Form: Ax + By = C3. Point-Slope form: y – y1 = m (x – x1)

3 Different Forms of a Linear Equation

Linear equation: • an equation whose graph is a line• the variable will have an exponent of 1

y- Intercept: • point where line crosses the y-axis

0

Identify parts in Slope-Intercept Form

X

Yy = mx + b

f(x) slope y-intercept

Graph y = 3 x + 2 4

1. Plot y-intercept

2. From known point, plot slope. (Rise over run)

3. Connect the 2 points with a line.

0

Practice: Slope Intercept Form

X

YGraph y = - 1 x – 2 2

1. Plot y-intercept

2. From known point, plot slope.

3. Connect the 2 points with a line.

If you know the slope of a line and the y-intercept, you can write the

equation of a line.

(0, 4)

Write a Linear Equation in Slope-Intercept Form

1. Find the slope of the line.

12

12

xx

yym

(0, 4)

(8, 1)

(0, 4)(8, 1) 8

3

8

3

80

14

m

2. Find the y-intercept.

(0, 4)

3. Substitute values into slope-intercept form of an equation.bmxy

48

3 xy

Write an equation of the line with slope and with a

y-intercept of 4.

25

y = mx + bWrite the slope-intercept equation

y = 2/5x + 4Substitute in know values

Write a Linear Equation in Slope-Intercept Form

Step 3 Write an equation in slope–intercept form,

using the given information

Write an equation for the line.

Step 1 Find the slope.

Write the slope formula: m = y2 – y1

x2 – x1

(0, 1)

m = 1 – (-1) = 2 0 – 3 -3

y = mx + b

y = - 2/3x + 1

Write a Linear Equation from a Graph

Step 2 Find the y-intercept.

Substitute in values

The base pay for a used car salesperson is $300 per week.

The salesperson also earns 15% commission on sales

made. The equation t = 300 + 0.15s relates total earnings (t)

to sales (s). Graph the equation.

Real-world and Slope-Intercept

1. What is the y-intercept?

t = 300 + 0.15s

(0, 300)

2. What is the slope?

100

1515.

3. Plot the y-intercept first. Plot slope, starting at y-intercept.