Question

graph the line.
$y-4=\frac{1}{4}(x-3)$

Explanation:

Step1: Identify point-slope form

The equation $y-4=\frac{1}{4}(x-3)$ uses the point-slope form $y-y_1=m(x-x_1)$, where $m$ is slope, $(x_1,y_1)$ is a point on the line.

Step2: Extract key values

From the equation: slope $m=\frac{1}{4}$, and the point on the line is $(3, 4)$.

Step3: Find a second point

Use the slope $\frac{1}{4}=\frac{\text{rise}}{\text{run}}$. Starting at $(3,4)$, add 1 to $y$ and 4 to $x$:
$x=3+4=7$, $y=4+1=5$. So a second point is $(7,5)$.

Step4: Graph the line

Plot the points $(3,4)$ and $(7,5)$, then draw a straight line through them.

Answer:

To graph the line:

1. Plot the point $(3, 4)$.
2. Using the slope $\frac{1}{4}$, plot a second point $(7, 5)$ (move 4 right and 1 up from $(3,4)$).
3. Draw a straight line through these two points.

The line can also be written in slope-intercept form as $y=\frac{1}{4}x+\frac{13}{4}$.