Question

Find the equation of line parallel to y=-2x+1 and passing through the point (2,4)

Answer 1

Answer:

$y=-2x+8$

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 x is 0)
• Parallel lines always have the same slopes

1) Determine the slope (m)

$y=-2x+1$

The given line has a slope of -2. Because parallel lines always have equal slopes, we know that the line parallel to this would also have a slope of -2. Plug this into $y=mx+b$:

$y=-2x+b$

2) Determine the y-intercept (b)

$y=-2x+b$

Plug in the given point (2,4) to solve for b

$4=-2(2)+b\\4=-4+b$

Add 4 to both sides to isolate b

$4+4=-4+b+4\\8=b$

Therefore, the y-intercept of the line is 8. Plug this back into $y=-2x+b$:

$y=-2x+8$

I hope this helps!