The equation for line j can be written as y= – 5/7 x–10. Line k, which is parallel to line j, includes the point ( – 9,5). What is the equation of line k?

Question

Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Answer 1

First you have to identify what you know about parallel lines: they have the same slope. In slope-intercept form, the slope is the number just before the x. In this case, the slope for both parallel lines would be -5/7.

Next, you plug in the information you know into point-slope form to find the equation for line k.

y-y₁=m(x-x₁)

The point you have been given (-9,5) can be plugged in for (x₁,y₁).

m is the slope, which we have already determined is -5/7

Plug in those numbers and solve so y is alone on the left side!

y-5=-5/7(x+9)

I bet you can solve for y now!

Answer 2

Line j is defined by the equation y=-57x-10, so the slope is -57 and the y-intercept is (0,-10).

Line k is parallel to line j, so it must have the same slope (-57), but a different y-intercept.

Given the conditions in the line above, the equation of line k must be y=-57x+b, where b is unknown.

Since we know that line k includes the point (-9,5), we can substitute those values in its equation:

5=-57(-9)+b

We can now simplify as follows:

5=513+b

And simplify further:

-508=b

Or b=-508.

We can now substitute our value for b into the equation, giving y=-57x-508.

If line k were perpendicular to line j, we would do exactly the same thing, except we would use the negative reciprocal of the slope, so we would use a slope of 1/57. In this case,our equation would be y=x/57+b.

Then we would substitute the coordinates of our point (-9,5) in the equation:

5=-9/57+b

Simplifying:

b=5 9/57

And we can substitute back into the equation: y=x/57+5 9/57.

To make the equation easier to read, we could write it as 57y=x+294.