Question

1. $f(x) = 2(x - 5) + 12$

form:

Explanation:

Step1: Simplify the linear function

First, expand and combine like terms to convert the function to slope-intercept form ($y=mx+b$).
$f(x) = 2(x - 5) + 12 = 2x - 10 + 12 = 2x + 2$

Step2: Identify key graph features

From $f(x)=2x+2$, the slope $m=2$ (rise 2, run 1) and y-intercept $b=2$ (the point $(0,2)$).

Step3: Find x-intercept

Set $f(x)=0$ to find where the line crosses the x-axis:
$0=2x+2 \implies 2x=-2 \implies x=-1$
This gives the point $(-1,0)$.

Step4: Plot and draw the line

Plot the y-intercept $(0,2)$ and x-intercept $(-1,0)$. Use the slope to find additional points (e.g., $(1,4)$, $(2,6)$) and draw a straight line through all points on the grid.

Answer:

The simplified function is $f(x)=2x+2$. To graph:

1. Plot the y-intercept $(0, 2)$
2. Plot the x-intercept $(-1, 0)$
3. Draw a straight line through these points, extending it across the grid (using the slope of 2 to verify additional points like $(1,4)$ or $(-2,-2)$)

Form: Slope-Intercept Form ($y=mx+b$)