Question

identify the graph of the given function:
$y = \frac{3x}{5} - 3$

Explanation:

Step1: Rewrite in slope-intercept form

The function is already in slope-intercept form $y=mx+b$:
$y = \frac{3}{5}x - 3$
Here, slope $m=\frac{3}{5}$, y-intercept $b=-3$.

Step2: Identify y-intercept point

The y-intercept is the point where $x=0$, so:
$(0, -3)$

Step3: Identify x-intercept point

Set $y=0$ and solve for $x$:
$0 = \frac{3}{5}x - 3$
$\frac{3}{5}x = 3$
$x = 3 \times \frac{5}{3} = 5$
So the x-intercept is $(5, 0)$.

Step4: Match to graph

The line has a positive shallow slope, crosses y-axis at $(0,-3)$ and x-axis at $(5,0)$, which matches graph C.

Answer:

C. The graph with positive shallow slope, crossing y-axis at (0, -3) and x-axis at (5, 0)