write the equation of the line in slope- intercept form

Question

1.) x-intercept = -4, y-intercept = 1

2.) x-intercept = 5, y-intercept = -2

Answer 1

Hello, Lavy,

I'll rewrite the two problems in a point format, to start. Each has two points described.

1.) x-intercept = -4, y-intercept = 1

(0, -4) and (1, 0)

2.) x-intercept = 5, y-intercept = -2

(0, 5) and (-2, 0)

Taking problem 1, the equation for a straight line is y = mx + b, where m is the slope, or rate of change as x changes value. From the two points, we see that when x goes from 0 to 1, that y goes from -4 to 0. The slope is sometimes referred to as the "rise over the run." The rise is the change in y. The run is the change in x. In this example the change in y (rise) is 4 ((0 - (-4)) when x (run) changes by 1 (1-0). The slope would be rise/run or 4/1 or 4.

This is the "m" in the equation, so we get

y = 4x + b

To find b, use one of the two points and solve for b:

0 = 4*1 + b

b = -4

So the equation is y = 4x -4

Do exactly the same for problem 2.

I hope this helps,

Bob

Answer 2

Slope intercept form is y=mx+b, where m is the slope and b is the y-intercept. To find the slope, you need to plug into the slope formula (y2-y1)/(x2-x1) using 2 coordinate points (x1,y1) and (x2,y2). When you are given the x-intercept and y-intercept, you are actually being given coordinates - the y value of the x-intercept is 0 and the x-coordinate for the y-intercept is also 0. For the first problem, this would mean that you have the points (-4,0) and (0,1) to plug into the slope formula. Once you get the slope and plug in for m, the b-value is just the y-intercept value.