Write the equation of the line, given the y- and x- intercepts. y-intercept (0,-6)x-intercept (-2,0)

y = -3x - 6

Step-by-step explanation:

Treat (0,-6) and (-2,0) as points on the line; it is not essential to recognize that they represent the x- and y-intercepts.  As we go from (-2,0) to (0,-6), x increases by 2 and y decreases by 6.  Thus, the slope of this line is m = rise / run = -6/2 = -3.

Write out the slope-intercept form:  y = mx + b.  Now subst. -3 for m, -6 for y and 0 for x, obtaining:  -6 = -3(0) + b.  Then b = -6, and the equation of this line is therefore y = -3x - 6.

Check:  If x=0, is y=-6?  Yes.  If y = 0, is x= -2?  Yes.

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