Question

Write the equation of the line that passes through the point (6,-2) and is parallel to the line y=1/3x+8

Answer 1

If a line is parallel to another it has the same slope. Since the equation y = 1/3x +8 is parallel to the line we are trying to find, our second line will have the slope of 1/3x as well

This is the equation of a line:

y = mx + b

m = slope = 1/3x

b = y intercept = unknown

We have to find b to make this equation complete. How do we do this?

First plug what you know into the equation: y = 1/3x + b

Second we must solve for b. To do this plug a point that passes through the line (in this case they said (6, -2) passes through the line) into the x and y of the equation:

-2 = 1/3(6) + b

Now solve for b!

-2 = 6/3 + b

-2 = 2 + b

- 2 - 2 = b

-4 = b

The equation parallel to y=1/3x + 8 and passes through point (6, -2) is y = 1/3x - 4

The image below is the two line one a coordinate plane. As you can see, they are parallel to each other

Hope this helped!