Question

graph this function:$f(x) = -2x - 16$graph this function:$f(x) = \frac{1}{2}x - 6$

Explanation:

Step1: Identify slope-intercept form

Both functions use $y=mx+b$, where $m$=slope, $b$=y-intercept.

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For $f(x) = -2x - 16$:

Step2: Find y-intercept ($b$)

$b=-16$, so plot point $(0, -16)$.

Step3: Use slope $m=-2$

Slope $\frac{\Delta y}{\Delta x} = \frac{-2}{1}$. From $(0,-16)$, move 1 right, 2 down to $(1, -18)$; or 8 left, 16 up to $(-8, 0)$ (x-intercept).

Step4: Draw line through points

Connect $(0,-16)$ and $(-8,0)$ (and extend).

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For $f(x) = \frac{1}{2}x - 6$:

Step2: Find y-intercept ($b$)

$b=-6$, so plot point $(0, -6)$.

Step3: Use slope $m=\frac{1}{2}$

Slope $\frac{\Delta y}{\Delta x} = \frac{1}{2}$. From $(0,-6)$, move 2 right, 1 up to $(2, -5)$; or 12 right, 6 up to $(12, 0)$ (x-intercept).

Step4: Draw line through points

Connect $(0,-6)$ and $(12,0)$ (and extend).

Answer:

1. For $f(x) = -2x - 16$:

• Y-intercept: $(0, -16)$
• X-intercept: $(-8, 0)$
• Draw a straight line through these two points, extending across the grid.

1. For $f(x) = \frac{1}{2}x - 6$:

• Y-intercept: $(0, -6)$
• X-intercept: $(12, 0)$
• Draw a straight line through these two points, extending across the grid.