Question

write an equation of the line that passes through (1,2) and is parallel to the line y = -5x + 4.
y = \square

Explanation:

Step1: Determine the slope of the parallel line

Parallel lines have the same slope. The given line is \( y = -5x + 4 \), which is in slope - intercept form \( y=mx + b \) (where \( m \) is the slope and \( b \) is the y - intercept). So the slope \( m \) of the line we want to find is also \( - 5 \).

Step2: Use the point - slope form to find the equation

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 \( m=-5 \) and the point \( (x_1,y_1)=(1,2) \). Substitute these values into the point - slope form:
\( y - 2=-5(x - 1) \)

Step3: Simplify the equation to slope - intercept form

First, distribute the - 5 on the right - hand side:
\( y - 2=-5x+5 \)
Then, add 2 to both sides of the equation to solve for \( y \):
\( y=-5x + 5+2 \)
\( y=-5x+7 \)

Answer:

\( y=-5x + 7 \)