slope of a line

Question

Find an equation of the line that has the same y-intercept as the line y + 4x - 8 = 0 and b. is parallel to the line 5x - 9y = 2 .

Answer 1

Hi there! Working with lines is always easiest when they are in slope-intercept form (y=mx+b). So the first thing I am going to do is solve both of these equations for y so they are in slope-intercept form:

y + 4x - 8 = 0 5x - 9y = 2

-4x +8 -4x +8 -5x -5x

y = -4x + 8 -9y = -5x + 2

/-9 /-9 /-9

y = 5/9 x - 2/9

Now, we want the y-intercept of our new line to have the same y-intercept of the first line. In slope intercept form (y = mx + b) the y-intercept is in the place of the "b". So, the y-intercept of the first line is 8. So, we can plug this into the "b" of our new line's equation:

y = mx + 8 Now to find our "m"....

We also want our new line to be parallel to the second equation. Parallel lines never intersect which means they have the same slope. The slope of a line in slope intercept form (y = mx + b) is in the place of the "m". So the slope of our second equation is 5/9. Putting this all into slope-intercept form the equation of our new line is:

y = 5/9 x + 8

If you have any questions don't hesitate to reach out!