Question

1. (8, 3); $y = -\frac{1}{4}x + 7$

Explanation:

Step1: Identify the task (assumed: find equation of line through (8,3) parallel/perpendicular? Let's assume parallel first, since slope is given. Parallel lines have same slope. Given line: \( y = -\frac{1}{4}x + 7 \), slope \( m = -\frac{1}{4} \).

Step2: Use point - slope form \( y - y_1 = m(x - x_1) \), where \( (x_1,y_1)=(8,3) \), \( m = -\frac{1}{4} \).

Substitute: \( y - 3 = -\frac{1}{4}(x - 8) \)

Step3: Simplify the equation.

Distribute: \( y - 3 = -\frac{1}{4}x + 2 \)
Add 3 to both sides: \( y = -\frac{1}{4}x + 5 \)
(If perpendicular, slope would be 4, but the given line has slope -1/4, and the point (8,3): let's check if (8,3) is on \( y = -\frac{1}{4}x + 7 \). Plug x = 8: \( y = -\frac{1}{4}(8)+7=-2 + 7 = 5
eq3 \). So maybe find the line through (8,3) parallel to \( y = -\frac{1}{4}x + 7 \), which we did as \( y = -\frac{1}{4}x + 5 \))

Answer:

If finding the parallel line through \((8,3)\) to \(y = -\frac{1}{4}x + 7\), the equation is \(y = -\frac{1}{4}x + 5\)