Question

What is the equation of the line in slope-intercept form? Line on a coordinate plane. The line runs through points begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma 5 end ordered pair.

Answer 1

Find the equation of the line connecting (0, 5) and (-2, 0).

As we go from the first point to the second, x decreases by 2 and y decreases by 5.  Thus, the slope of this line is m = rise / run = -5/(-2), or 5/2.

Starting with the general equation of a line in slope-intercept form, y = mx + b, substitute the knowns as appropriate to determine the value of b:

y= mx + b => 5 = (5/2)(0) + b.  Then b = 5, and the desired equation is

y = (5/2)x + 5.

Check this!  If we subst. the coordinates of (-2,0) into this equation, is the equation true?

0 = (5/2)(-2) + 5

Yes.  So, y = (5/2)x + 5 is the desired equation.