© william james calhoun, 2001 6-4: writing linear equations in slope-intercept form objectives: you...

© William James Calhoun, 2001

6-4: Writing Linear Equations in Slope-Intercept Form

OBJECTIVES:You will be able to determine the x- and y-intercepts of linear graphs from their equations and write equations in slope-intercept form.

What is an intercept?

Simply put, an intercept is a point at which the graph of an equation crosses an axis.

In the linear equations we will be dealing with, the graphed line either:(1) crosses the x-axis only (vertical line),(2) crosses the y-axis only (horizontal line), or(3) crosses both the x- and y-axes.

We label the crossing of the x-axis the “x-intercept” and the y-axis the “y-intercept”.



Look at the graphs below.

When the intercepts are identified and labeled, do you see anything repetitive about the x- and y-intercept points?

y-intercept(0, 2)

x-intercept(-2, 0)

y-intercept(0, -3)

x-intercept(-6, 0)

y-intercept(0, 3)

x-intercept none

The x-value of the coordinate for the y-intercept is always zero.The y-value of the coordinate for the x-intercept is always zero.So, the x-intercept is the point where y = 0, and the y-intercept is the point where x = 0.



EXAMPLE 1: Find the x- and y-intercepts of the graph of3x + 4y = 6.

The x-intercept is the point where y = 0.Rewrite equation setting y = 0.

The y-intercept is the point where x = 0.Rewrite equation setting x = 0.

3x + 4y = 63x + 4(0) = 63x + 0 = 63x = 6

Solve for x and write answer as an ordered pair.

3 3x = 2x-intercept: (2, 0)

3x + 4y = 63(0) + 4y = 60 + 4y = 64y = 6

Solve for y and write answer as an ordered pair.

4 4x = 6/4 = 3/2

y-intercept: (0, 3/2)Or, you can use the CPM:(1) Find the x-intercept by covering up the y’s and solve for x.(2) Find the y-intercept by covering up the x’s and solve for y.



The answers to that last example were given in ordered pair form.

The book does not present its answers as ordered pairs.

Keep this in mind while checking your homework problems.

You can give me your answer in either intercept form:y = 3 and x = -2

or coordinate form:(0, 3) and (-2, 0)

Just make sure you label clearly what you are doing.


From the graph below, take the point (0, b) - which is the y-intercept - and plug that point into the point-slope formula.

y - y1 = m(x - x1) y - b = m(x - 0)

Solve this for y to get something new that you must know…

The Slope-Intercept Form.

y - b = mx - 0y - b = mx

+b +b

y = mx + b

This form of the linear equation is easy to graph.Notice the “m” is the # with the x, and m is slope. Also, the # at the end, b, is the y-intercept.

Now for a new form to write equations in.

We will start with a picture, label a point on the graph, and then plug the information into the point-slope form.




You must memorize this form of a linear equation and know that m is the slope and b is the y-intercept.

EXAMPLE 2: Write an equation of a line in slope-intercept form if the line has a slope of 2/3 and a y-intercept of 6. Then write the equation in standard form.Plug the slope and y-intercept into the slope-intercept form.

y = mx + b

y = x +(2/3) (6)

Now, rewrite in standard form.

3y = 2x + 18-2x -2x

-2x + 3y = 18 2x - 3y = -18

Given the slope m and ht ey-intercept b of a line, the slope-intercept form of an equation of the line is

y = mx + b.

6.4.1 SLOPE-INTERCEPT FORM OF A LINEAR EQUATION

2y x 6

3

23(y) x 6 3

3

63y x 18

3



EXAMPLE 3: Find the slope and y-intercept of the graph of 5x - 3y = 6.

5x - 3y = 6-5x -5x

-3y = -5x + 63 3 slope

5/3

y-int

-2

The slope-intercept form of the equation shows the slope and intercept in an easy-to-see format.So, we will get this equation into slope-intercept form.To do this, you solve the equation for y, keeping certain things in order.

This is your answer.

5 6y x

3 3

5y x 2

3

Now for an example that does a little bit of everything we have learned so far in this chapter.



EXAMPLE 4: Write the slope-intercept and standard forms of the equation for a line that passes through (-3, -1) and (6, -4).

1) Find the slope.

2) Plug slope and one point into formula.

y - y1 = m(x - x1)

3) Put this in slope-intercept form.

y + 1 = -1/3x - 1-1 -1y = -1/

3x - 2

4) Put the equation in standard form.

3(y) = (-1/3x - 2)3

3y = -1x - 6+x +xx + 3y = -6

2 1

2 1

y ym

x x

4 ( 1)

6 ( 3)

4 1

6 3

3 1

9 3

1y ( 1) (x ( 3))

3

1y 1 (x 3)

3



HOMEWORK

Page 350#19 - 49 odd

© william james calhoun, 2001 6-4: writing linear equations in slope-intercept form objectives: you...

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