Question

question 8 of 10, step 2 of 2
consider the following function.
step 2 of 2: find two points on the line to graph the function.
q(x) = x - \frac{(3 + 8x)}{6}
answer

Explanation:

Step1: Simplify the given function

First, expand and combine like terms:

$$\begin{align*} q(x) &= x - \frac{(3 + 8x)}{6}\\ &= \frac{6x}{6} - \frac{3 + 8x}{6}\\ &= \frac{6x - 3 - 8x}{6}\\ &= \frac{-2x - 3}{6}\\ &= -\frac{1}{3}x - \frac{1}{2} \end{align*}$$

Step2: Find x=0 (y-intercept)

Substitute $x=0$ into the simplified function:

$$ q(0) = -\frac{1}{3}(0) - \frac{1}{2} = -\frac{1}{2} $$

This gives the point $(0, -\frac{1}{2})$.

Step3: Find x=3 (a convenient x-value)

Substitute $x=3$ into the simplified function:

$$ q(3) = -\frac{1}{3}(3) - \frac{1}{2} = -1 - \frac{1}{2} = -\frac{3}{2} $$

This gives the point $(3, -\frac{3}{2})$.

Answer:

Two points on the line are $\boldsymbol{(0, -\frac{1}{2})}$ and $\boldsymbol{(3, -\frac{3}{2})}$ (other valid points are also acceptable)