Question

Find the equation of the line that is parallel to y = 4 - 3x and passes through the point (1,5).

Answer 1

Answer:

$y=-3x+8$

Step-by-step explanation:

Hi there!

What we need to know:

• Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
• Parallel lines always have the same slope

1) Determine the slope (m)

$y = 4 - 3x\\y = -3x+4$

Given this equation, we can identify the slope to be -3 since it's in the place of m in $y=mx+b$.

Because parallel lines have the same slope, -3 is therefore the slope of the line we're currently solving for. Plug this into $y=mx+b$:

$y=-3x+b$

2) Determine the y-intercept (b)

$y=-3x+b$

Plug in the given point (1,5) and solve for b:

$5=-3(1)+b\\5=-3+b\\8=b$

Therefore, the y-intercept is 8. Plug this back into $y=-3x+b$:

$y=-3x+8$

I hope this helps!