Question

graph this line:
$y + 7 = \frac{1}{5}(x - 2)$
click to select points on the graph.

Explanation:

Step1: Identify point from point-slope form

The equation $y + 7 = \frac{1}{5}(x - 2)$ is in point-slope form $y-y_1=m(x-x_1)$, so one point on the line is $(2, -7)$.

Step2: Find a second point using slope

The slope $m=\frac{1}{5}$, meaning for a 5-unit increase in $x$, $y$ increases by 1. Starting from $(2, -7)$:
$x=2+5=7$, $y=-7+1=-6$. So a second point is $(7, -6)$.

Step3: Verify y-intercept (optional check)

Rewrite equation to slope-intercept form:
$y = \frac{1}{5}x - \frac{2}{5} - 7$
$y = \frac{1}{5}x - \frac{2}{5} - \frac{35}{5}$
$y = \frac{1}{5}x - \frac{37}{5}$
The y-intercept is $(0, -\frac{37}{5}) = (0, -7.4)$, which aligns with the line through the two points.

Answer:

Plot the points $(2, -7)$ and $(7, -6)$ (or $(0, -7.4)$), then draw a straight line passing through them to graph the line.