Question

1. write an equation that parallel to $y = -4x - 1$ and passes through the point $(-3, 5)$

Explanation:

Step1: Recall slope of parallel lines

Parallel lines have equal slopes. The given line is \( y = -4x - 1 \), which is in slope - intercept form \( y=mx + b \) where \( m \) is the slope. So the slope \( m \) of the line we want to find is also \( - 4 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1) \) is a point on the line and \( m \) is the slope. We know that \( m=-4 \), \( x_1=-3 \) and \( y_1 = 5 \). Substitute these values into the point - slope form:
\( y - 5=-4(x - (-3)) \)
Simplify the equation inside the parentheses: \( y - 5=-4(x + 3) \)

Step3: Convert to slope - intercept form (optional, but common)

Distribute the - 4 on the right - hand side: \( y - 5=-4x-12 \)
Add 5 to both sides of the equation: \( y=-4x-12 + 5 \)
Simplify the constants: \( y=-4x-7 \)

Answer:

\( y=-4x - 7 \)