Question

1. what is the equation of the line that passes through the point (-1, 5) and is parallel to the line y = -3x + 5? a. $y = -\frac{x}{3} + \frac{14}{3}$ b. $y = 3x + 8$ c. $y = -3x + 2$ d. $y = \frac{x}{3} + \frac{16}{3}$

Explanation:

Step1: Determine the slope

Parallel lines have the same slope. The given line \( y = -3x + 5 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope. So the slope \( m=-3 \). The equation of the line we want to find will also have a slope of \( - 3 \).

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 \( m=-3 \) and the point \( (-1,5) \) lies on the line, so \( x_1=-1 \) and \( y_1 = 5 \).

Substitute these values into the point - slope form:
\( y-5=-3(x - (-1)) \)
\( y - 5=-3(x + 1) \)

Step3: Simplify to slope - intercept form

Expand the right - hand side:
\( y-5=-3x-3 \)

Add 5 to both sides of the equation:
\( y=-3x-3 + 5 \)
\( y=-3x + 2 \)

Answer:

C. \( y=-3x + 2 \)