Question

graph this line:
$y + 4 = \frac{7}{2}(x + 2)$
click to select points on the graph.

Explanation:

Step1: Identify point from point-slope form

The equation $y + 4 = \frac{7}{2}(x + 2)$ is in point-slope form $y - y_1 = m(x - x_1)$, so one point on the line is $(-2, -4)$.

Step2: Find second point using slope

Slope $m = \frac{7}{2} = \frac{\text{rise}}{\text{run}}$. From $(-2, -4)$, add 2 to $x$ and 7 to $y$:
$x = -2 + 2 = 0$, $y = -4 + 7 = 3$.
Second point is $(0, 3)$.

Step3: Verify with slope-intercept form (optional)

Rewrite equation to slope-intercept $y=mx+b$:
$y = \frac{7}{2}x + 7 - 4$
$y = \frac{7}{2}x + 3$
This confirms y-intercept $(0,3)$ and slope $\frac{7}{2}$.

Answer:

Plot the points $(-2, -4)$ and $(0, 3)$, then draw a straight line through them to graph the line.