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Big Ideas Math Integrated I, 2016
BI
Big Ideas Math Integrated I, 2016 View details
5. Graphing Linear Equations in Slope-Intercept Form
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Exercise 58 Page 144

In what form must you be able to write all linear functions?

Linear function, see solution.

Practice makes perfect

Consider the given equation. x=3+15yWe want to determine whether the equation represents a linear or nonlinear function. To do so, remember that all linear equations must be able to be written in slope-intercept form. y=mx+b Here, m represent the slope and b indicates the y-intercept. These are the general characteristics or parameters of the line. If we change either of these parameters, the function's graph will change too. Let's solve the given equation for y to see if it can be written in this form.

x=3+15y
RearrangeEqn

Rearrange equation

3+15y=x
SubEqn

LHS-3=RHS-3

15y=x-3
DivEqn

.LHS /15.=.RHS /15.

y=x-3/15
WriteDiffFrac

Write as a difference of fractions

y=x/15-3/15
ReduceFrac

a/b=.a /3./.b /3.

y=x/15-1/5
MoveRightFacToNumOne

1/b* a = a/b

y=1/15x-1/5

This equation is now in slope-intercept form with a slope of 115 and a y-intercept of - 15. Therefore, the function is linear.

Extra

 Linear Function
More information about linear functions can be found on the following pages.

Subchapter links expand_more
arrow_right Communicate Your Answer p.135
3
arrow_right Monitoring Progress p.136-140
Monitoring Progress 1 (Page 136)
Monitoring Progress 2 (Page 136)
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Monitoring Progress 9 (Page 139)
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arrow_right Exercises p.141-144
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