Lesson 4.1: Slope intercept form

Slope-Intercept Form:
y=mx+b

Understanding and applying the slope-intercept form of a linear equation, y = mx + b, is essential in algebra. This form allows us to easily identify the slope and y-intercept of a line, making it a powerful tool in graphing and solving equations.

Multiple Choice

Which of the following functions is written in slope-intercept form?

• y = mx + b

• $$y=ax^2+bx+c$$

• y = bx - m

• Ax + By = C

Dropdown

In a slope intercept form equation y = mx + b, the m is the ​

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and the b is the ​

Select answer

.

​Find the slope and the y intercept of the following:

​1. y=-2/3 x + 4

​2. y = 3x - 5

​3. y = x + 2

​b=

m=

​b=

m=

b=

m=

Dropdown

The equation y = -4x + 5 is in slope intercept form. The y intercept of the equation is ​ ​

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and the slope of the equation is​ ​

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.

Dropdown

The equation y = 2x - 3 is in slope intercept form. The y intercept of the equation is ​

Select answer

and the slope of the equation is​

Select answer

.

Graphing Linear Equations with y = mx + b

Use y = mx + b, where m is the slope and b is the y-intercept.
Step #1: Plot the y-intercept on the graph with the value of b.
Step #2 Use the slope (the value of m) to find additional points.
Step #3 Connect the points to create a straight line.

​If the equation is in slope intercept form graph your y interecept coordinate, then Rise and Run from that point according to slope.

​y = x - 2

Examples:

1. y= -x - 3

2. y= -1/3 x + 2

3. y = 2/3 x

Graphing

$$y=-\frac{1}{2}x+6$$

Graphing

$$y=2x-5$$

Graphing

$$y=x+4$$

Graphing

$$y=-\frac{3}{4}x-6$$

Graphing

$$y=\frac{5}{6}x-4$$

Graphing

$$y=-x$$

​Not all equations are ready to graph.

You may have to rewrite the equation in slope intercept form to easily graph with the m and the b. Example:

​1. y - 1 = 3x

Graphing

$$y-3=x-9$$

​Not all equations are ready to graph.

You may have to rewrite the equation in slope intercept form to easily graph with the m and the b. Examples:

​2. 3y = x - 6

​1. 4y = 2x - 12

Graphing

$$3y=x-9$$

Graphing

$$2y=5x+4$$

​Not all equations are ready to graph.

You may have to rewrite the equation in slope intercept form to easily graph with the m and the b. Example:

​3. -2y + 8 = 3x

Graphing

$$4y+6=12x-2$$

End of section.