Exercise 116 Page 297

Practice makes perfect

a Equations in slope-intercept form follow a specific format, where m represents the slope of the line and b is the y-intercept.

y= mx+ bLet's rewrite our equation so that it more closely resembles this format. This will make it easier to identify the features of the equation.

2x+7y=14

SubEqn

LHS-2x=RHS-2x

7y=- 2x+14

DivEqn

.LHS /7.=.RHS /7.

y=- 2x/7 +2

MoveNegNumToFrac

Put minus sign in front of fraction

y=- 2x/7 +2

MovePartNumRight

a* b/c=a/c* b

y=- 2/7x +2

Now our equation is in the slope-intercept form, so we can highlight the slope m and y-intercept b. y= - 2/7x+ 2 We can see that the slope is - 27 and the y-intercept is 2.

b Equations in slope-intercept form follow a specific format, where m represents the slope of the line and b is the y-intercept.

y= mx+ bLet's rewrite our equation so that it more closely resembles this format. This will make it easier to identify the features of the equation.

y=6-x/3

CommutativePropAdd

Commutative Property of Addition

y=- x/3+6

MovePartNumRight

a* b/c=a/c* b

y=- 1/3x+6

Now our equation is in the slope-intercept form, so we can highlight the slope m and y-intercept b. y= - 1/3x+ 6 We can see that the slope is - 13 and the y-intercept is 6.

c Equations in slope-intercept form follow a specific format, where m represents the slope of the line and b is the y-intercept.

y= mx+ bLet's rewrite our equation so that it more closely resembles this format. This will make it easier to identify the features of the equation.

y=10x-2/2

WriteDiffFrac

Write as a difference of fractions

y=10x/2-2/2

MovePartNumRight

a* b/c=a/c* b

y=10/2x-2/2

CalcQuot

Calculate quotient

y=5x-1

Now our equation is in the slope-intercept form, so we can highlight the slope m and y-intercept b. y= 5x - 1 ⇔ y= 5x+( - 1) We can see that the slope is 5 and the y-intercept is - 1.

d Equations in slope-intercept form follow a specific format, where m represents the slope of the line and b is the y-intercept.

y= mx+ b The given equation is already in this form. Below we have highlighted the slope m and y-intercept b. y= 3x+ 0 We can see that the slope is 3 and the y-intercept is 0.