do you know the equation of a line that is parallel to y=6x+1 and passes through the poin (-7,1)

Answer 1

Remember that equations of parallel lines have equal slopes, therefore, the slope of the second equation is 6.

Now you have two options:

1) You can use the slope and the given point to write an equation in Point-Slope form

y - y₁ = m(x - x₁)

y - 1 = 6(x - (-7))

y - 1 = 6(x + 7)

y = 6(x + 7) + 1

OR

2) You can use the slope and the given point to find the y-intercept and then write the equation in Slope-Intercept form

y = mx + b

1 = (6)(-7) + b

1 = -42 + b

43 = b

y = 6x +43

While they may look different, both equations are equivalent :)

Answer 2

Lines that are parallel have the same slope. So the slope of the new line is 6. Now we can use point-slope form to find the equation of the new line.

Point-Slope Form:

y-y₁ = m(x-x₁)

Where (x₁,y₁) is the point (-7,1) and m is the slope 6.

so the equation is:

y-1=6(x-(-7))

y-1=6(x+7)

If you want to put this into slope-intercept form just distribute the 6 and add 1 to both sides of the equation

y-1=6x+42

y=6x+43

The Correct Answer is: y=6x+43