Question

consider the following function.
$q(x) = 5x - \frac{(3 + 5x)}{6}$
step 2 of 2: find two points on the line to graph the function.
answer 2 points
any lines or curves will be drawn once all required points are plotted.

Explanation:

Step1: Simplify the function

First, expand and combine like terms:

$$\begin{align*} g(x)&=5x - \frac{3+5x}{6}\\ &=\frac{30x}{6} - \frac{3+5x}{6}\\ &=\frac{30x - 3 - 5x}{6}\\ &=\frac{25x - 3}{6}\\ &=\frac{25}{6}x - \frac{1}{2} \end{align*}$$

Step2: Find x=0 intercept

Substitute $x=0$ into the simplified function:

$$ g(0)=\frac{25}{6}(0) - \frac{1}{2}=-\frac{1}{2} $$

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

Step3: Find x=6 point

Substitute $x=6$ to avoid fractions:

$$ g(6)=\frac{25}{6}(6) - \frac{1}{2}=25 - \frac{1}{2}=\frac{49}{2} $$

This gives the point $(6, \frac{49}{2})$.

Answer:

Two points on the line are $\boldsymbol{(0, -\frac{1}{2})}$ and $\boldsymbol{(6, \frac{49}{2})}$ (other valid points are also acceptable, e.g., $(1, \frac{11}{3})$)