Question

graph this line:
$y + 1 = \frac{1}{4}(x - 6)$
click to select points on the graph.

Explanation:

Step1: Identify point-slope form

The equation $y + 1 = \frac{1}{4}(x - 6)$ is in point-slope form $y - y_1 = m(x - x_1)$, where $(x_1,y_1)$ is a point on the line, and $m$ is the slope.

Step2: Extract first point

From the equation, $x_1=6$, $y_1=-1$. So the first point is $(6, -1)$.

Step3: Use slope to find second point

Slope $m=\frac{1}{4}$, meaning $\frac{\text{rise}}{\text{run}}=\frac{1}{4}$. Starting from $(6, -1)$, add 4 to $x$ and 1 to $y$: $x=6+4=10$, $y=-1+1=0$. The second point is $(10, 0)$.

Step4: Verify with y-intercept (optional)

Rewrite equation to slope-intercept form:
$y + 1 = \frac{1}{4}x - \frac{6}{4}$
$y = \frac{1}{4}x - \frac{3}{2} - 1$
$y = \frac{1}{4}x - \frac{5}{2}$
When $x=0$, $y=-\frac{5}{2}=-2.5$, so a third point is $(0, -2.5)$.

Answer:

Plot the points $(6, -1)$, $(10, 0)$, and $(0, -2.5)$, then draw a straight line through them to graph the line.