Question

graph this line:
$y + 5 = -\frac{1}{4}(x - 1)$
click to select points on the graph.

Explanation:

Step1: Identify point from point-slope form

The equation $y + 5 = -\frac{1}{4}(x - 1)$ is in point-slope form $y - y_1 = m(x - x_1)$, so one point on the line is $(1, -5)$.

Step2: Find a second point using slope

The slope $m = -\frac{1}{4}$, meaning for a run of $4$, the rise is $-1$. Starting from $(1, -5)$:
$x = 1 + 4 = 5$, $y = -5 + (-1) = -6$.
So a second point is $(5, -6)$.

Step3: Verify with y-intercept (optional)

Rewrite equation in slope-intercept form:
$y = -\frac{1}{4}x + \frac{1}{4} - 5$
$y = -\frac{1}{4}x - \frac{19}{4}$
When $x=0$, $y = -\frac{19}{4} = -4.75$, so the y-intercept is $(0, -4.75)$.

Answer:

Plot the points $(1, -5)$, $(5, -6)$, and $(0, -4.75)$, then draw a straight line through them to graph the line.