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Question Find the slope and intercepts of the linear function g(x)=−13x+5g(x) = \frac{-1}{3}x + 5.

Studdy Solution

STEP 1

Assumptions
1. The function given is g(x)=−13x+5g(x)=\frac{-1}{3} x+5.
2. The standard form of a linear equation is y=mx+by=mx+b, where mm is the slope and bb is the y-intercept.
3. To find the x-intercept, we set y=0y=0 and solve for xx.

STEP 2

Identify the slope of the function by comparing the given function to the standard form of a linear equation.
Slope (m)=−13Slope\,(m) = \frac{-1}{3}

STEP 3

State the slope of the function.
The slope of the function is −13\frac{-1}{3}.

STEP 4

Identify the y-intercept of the function by comparing the given function to the standard form of a linear equation.
y-intercept (b)=5y\text{-intercept}\,(b) = 5

STEP 5

State the y-intercept of the function.
The y-intercept of the function is 5.

STEP 6

To find the x-intercept, set g(x)=0g(x)=0 and solve for xx.
0=−13x+50 = \frac{-1}{3} x + 5

STEP 7

Subtract 5 from both sides of the equation to isolate the term with xx.
−5=−13x-5 = \frac{-1}{3} x

STEP 8

Multiply both sides of the equation by −3-3 to solve for xx.
15=x15 = x

STEP 9

State the x-intercept of the function.
The x-intercept of the function is 15.
Solution: a) The slope of the function is −13\frac{-1}{3}. b) The y-intercept of the function is 5, and the x-intercept is 15.

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