Question

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

Explanation:

Step1: Identify point from point-slope form

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

Step2: Find a second point using slope

Slope $m=\frac{1}{4}$, so from $(1, -4)$, move 4 right and 1 up: $x=1+4=5$, $y=-4+1=-3$. The second point is $(5, -3)$.

Step3: Plot and connect points

Mark $(1, -4)$ and $(5, -3)$ on the grid, then draw a straight line through them.

Answer:

The line passes through points $(1, -4)$ and $(5, -3)$; a straight line connecting these points (and extending infinitely in both directions) is the graph of $y + 4 = \frac{1}{4}(x - 1)$.