Question

1. write and graph the equation of the line through the point (-4,2) parallel to line n in graph below.

Explanation:

Step1: Find slope of line n

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For two - points $(0,-2)$ and $(8,0)$ on line $n$, we have $m=\frac{0-(-2)}{8 - 0}=\frac{2}{8}=\frac{1}{4}$.

Step2: Use point - slope form

Parallel lines have the same slope. The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(-4,2)$ and $m = \frac{1}{4}$, we get $y - 2=\frac{1}{4}(x+4)$.

Step3: Convert to slope - intercept form

Expand the right - hand side: $y - 2=\frac{1}{4}x + 1$. Then add 2 to both sides to get $y=\frac{1}{4}x+3$.

Step4: Graph the line

1. Plot the y - intercept $(0,3)$.
2. Use the slope $\frac{1}{4}$ (rise 1, run 4) to find another point. Starting from $(0,3)$, move 4 units to the right and 1 unit up to get the point $(4,4)$. Draw a line through these two points.

Answer:

The equation of the line is $y=\frac{1}{4}x + 3$.