Question

which of the following statements about the graph of $y = 3x - 5$ are true? select all that apply.
a. the $y$-intercept is $-5$.
b. the $x$-intercept is $3$.
c. $(2, 1)$ is a point on the graph.
d. as the $x$-values increase, the $y$-values also increase.

Explanation:

Step1: Check y-intercept

The equation is in slope-intercept form $y=mx+b$, where $b$ is the y-intercept. Here, $b=-5$. So the y-intercept is $-5$.

Step2: Calculate x-intercept

Set $y=0$, solve for $x$:
$$0=3x-5$$
$$3x=5$$
$$x=\frac{5}{3}$$
The x-intercept is $\frac{5}{3}$, not 3.

Step3: Verify point (2,1)

Substitute $x=2$ into $y=3x-5$:
$$y=3(2)-5=6-5=1$$
Since $y=1$ when $x=2$, (2,1) is on the graph.

Step4: Analyze slope trend

The slope $m=3$, which is positive. A positive slope means as $x$ increases, $y$ increases.

Answer:

A. The y-intercept is -5.
C. (2, 1) is a point on the graph.
D. As the x-values increase, the y-values also increase.