Question

graph this line:
$y + 6 = \frac{1}{5}(x - 1)$
click to select points on the graph.

Explanation:

Step1: Identify point from point-slope form

The equation $y + 6 = \frac{1}{5}(x - 1)$ is in point-slope form $y-y_1=m(x-x_1)$, so one point is $(1, -6)$.

Step2: Find a second point using slope

Slope $m=\frac{1}{5}$, so from $(1, -6)$, move 5 right and 1 up: $x=1+5=6$, $y=-6+1=-5$. The second point is $(6, -5)$.

Step3: Verify y-intercept (optional check)

Rewrite equation to slope-intercept form:
$y = \frac{1}{5}x - \frac{1}{5} - 6$
$y = \frac{1}{5}x - \frac{31}{5}$
When $x=0$, $y=-\frac{31}{5}=-6.2$, which aligns with the line through the two points.

Answer:

Plot the points $(1, -6)$ and $(6, -5)$, then draw a straight line passing through them (the line will also pass through $(0, -6.2)$ as a third reference point).