Question

which equation represents the graph?
options:
$y = -dfrac{3}{2}x + 5$
$y = -dfrac{2}{3}x + 3$

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0, -3)$, so $b=-3$.

Step2: Calculate slope (m)

Use two points $(0, -3)$ and $(4.5, 0)$:
$$m=\frac{0 - (-3)}{4.5 - 0}=\frac{3}{4.5}=\frac{2}{3}$$

Step3: Write slope-intercept form

Substitute $m=\frac{2}{3}$ and $b=-3$ into $y=mx+b$:
$$y=\frac{2}{3}x - 3$$

Step4: Verify against options

Rewrite the equation to match structure:
$$y=\frac{2}{3}x - 3$$
Check that the given incorrect options have negative slopes (contradicting the positive slope of the line) and wrong intercepts. The correct equation matching the graph is $y=\frac{2}{3}x - 3$, which is the valid equation for the line shown.

Answer:

$y=\frac{2}{3}x - 3$
(Note: The provided options do not include the correct equation; the line has a positive slope and y-intercept at -3, which does not match the two listed negative-slope, positive-intercept options.)