Math  /  Algebra

QuestionA linear function is given. Complete parts (a)-(d). h(x)=12x6h(x)=\frac{1}{2} x-6 (a) Determine the slope and yy-intercept of the function.
The slope is 12\frac{1}{2}. (Type an integer or a simplified fraction.) The yy-intercept is \square . (Type an integer or a simplified fraction.)

Studdy Solution

STEP 1

1. The function h(x)=12x6 h(x) = \frac{1}{2}x - 6 is in the slope-intercept form, y=mx+b y = mx + b .
2. In the slope-intercept form, m m represents the slope and b b represents the y y -intercept.

STEP 2

1. Identify the slope of the function.
2. Identify the y y -intercept of the function.

STEP 3

The slope-intercept form of a linear function is given by:
y=mx+b y = mx + b
where m m is the slope and b b is the y y -intercept.

STEP 4

For the function h(x)=12x6 h(x) = \frac{1}{2}x - 6 , compare it to the slope-intercept form y=mx+b y = mx + b .
The coefficient of x x is 12 \frac{1}{2} , which is the slope m m .

STEP 5

The constant term in the function h(x)=12x6 h(x) = \frac{1}{2}x - 6 is 6-6, which is the y y -intercept b b .
The y y -intercept is 6-6.

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