QuestionA linear function is given. Complete parts (a)-(d). $h(x)=4 x+2$ (a) Determine the slope and $y$ -intercept of the function.
The slope is $\square$ (Type an integer or a simplified fraction.)

Studdy Solution

STEP 1

1. The function $h(x) = 4x + 2$ is in the slope-intercept form of a linear equation, which is $y = mx + b$ .
2. In the slope-intercept form, $m$ represents the slope and $b$ represents the y-intercept.

STEP 2

1. Identify the slope from the linear equation.
2. Identify the y-intercept from the linear equation.

STEP 3

Identify the slope from the linear equation $h(x) = 4x + 2$ .
The slope-intercept form is given by $y = mx + b$ , where $m$ is the slope. In the equation $h(x) = 4x + 2$ , the coefficient of $x$ is $4$ .
Thus, the slope $m$ is:
$m = 4$

STEP 4

Identify the y-intercept from the linear equation $h(x) = 4x + 2$ .
In the slope-intercept form $y = mx + b$ , $b$ is the y-intercept. In the equation $h(x) = 4x + 2$ , the constant term is $2$ .
Thus, the y-intercept $b$ is:
$b = 2$
The slope is $\boxed{4}$ .

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