Find an equation of the line that (a) has y-intercept of 2 and (b) is parallel to the line -5x-9y=-10

Question

Find an equation of the line that (a) has y-intercept of 2 and (b) is parallel to the line -5x-9y=-10.Write your answer in the form y=mx+b.

y=_____x+_____

Answer 1

Find the slope of the line in standard from that is provided.

Parallel lines have the same slope, Perpendicular lines have the negative reciprocal.

once you get the slope, substitute for m, and use 2 as your new b value in Y=mx+b.

Answer 2

In the form y = Mx + b, m is the slope and b is the y intercept. The problem states that the y intercept is 2.

parallel lines have equal slopes. If you rearrange the given equation by solving for y you will have the equation in y = Mx. + b form.

-5x - 9y = -10

+5x. +5x

becomes. -9y = 5x -10. Then to get y by itself divide both sides of the equation by -9

y = (-5/9)x + (10/9). Therefore the slope of the given line is -5/9

the equation of the line parallel to the given line with y intercept of 2 is

y = (-5/9)x +2

Answer 3

Parallel lines always have the same slopes

First convert -5x-9y=-10 to y= form

9y= -5x + 10

y= -5/9x + 10/9

slope of new line is -5/9

y intercept given is 2

y = -5/9x + 2

done!

Answer 4

Find an equation of the line that has y-intercept of 2 and is parallel to the line -5x - 9y = -10

1. If a line has a y-intercept of 2, then the line passes through the point (0, 2)
2. If a line is parallel to another line, then the lines have the same slope but different y-intercepts
3. -5x - 9y = -10
4. -5x - 9y + 5x = -10 + 5x
5. -9y = 5x - 10
6. (-9y/-9) = (5x/-9) - (10/-9)
7. y = (-5/9)x + (10/9)
8. m = (-5/9)
9. The slope of our resulting line should be (-5/9) to be parallel to the given line
10. Our resulting equation in Slope-Intercept Form is y = (-5/9)x + b
11. We know our resulting line must pass through (0, 2), so we can substitute this ordered pair into our linear equation to solve for b
12. y = (-5/9)x + b
13. (2) = (-5/9)*(0) + b
14. b = 2

The equation of the line that has y-intercept of 2 and is parallel to the line -5x - 9y = -10 is y = (-5/9)x + 2