Question

f(x)=54​x−4 A. The slope is (Simplify your answer. Type an integer or a fraction.) B. The slope is undefined. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The y-intercept is (Simplify your answer. Type an integer or a fraction.) B. There is no y-intercept. Use the graphing tool to graph the equation.

Answer 1

Explanation:

Find the Equation of the Line:

y=mx+b

by solving for y using the Point Slope Equation.

y−y1=m(x−x1)

y−3=−125(x−2)

y−3=−125x−(−125×2)

y−3=−125x−−245

y−3=−125x+245

y=−125x+245+3

y=−125x+395

m=−125

b=395

In decimals:

y=−2.4x+7.8

Standard Form of a Linear Equation

Ax+By=C

Starting with y = mx + b

y=−125x+395

Multiply through by the common denominator, 5, to eliminate the fractions:

5y=−12x+39

Then rearrange to the Standard Form Equation:

12x+5y=39

A=12

B=5

C=39

y-Intercept, when x = 0

y=mx+b

y=−125x+395

When x = 0

y=−125×0+395

y=395

y-intercept=395

(x,y)=(0,395)

In decimals:

(x,y)=(0,7.8)

x-Intercept, when y = 0

y=mx+b

y=−125x+395

When y = 0

0=−125x+395

125x=395

x=395×512

x=3912

x=134

x-intercept=134

(x,y)=(134,0)

In decimals:

(x,y)=(3.25,0)