Question

What is the equation of the line that passes through the points (-4,3) and (2,-6)

Answer 1

Answer: y = -1.5x - 3

Step-by-step explanation:

We'll assume this is a straight line, with the form y=mx+b. m is the slope (the rate that y changes with a change in x) and b is the y-intercept (the value of y when x=0).

Once we can determine both m and b, we'll have an equation that answers this question. First, m.

m, the slope, is known as the Rise/Run. We can use the two given points to calculate this value. Take the two points, (-4,3) and (2,-6), and calculate the change in x (the Run), by subtrating the initial point (I'll choose (-4,3)) from the final point ((2,-6)). For x that is: 2-(-4) = 6. For y: -6-3 = -9. When x moved +6 units, y went down by 9, or -9. The slope is the Rise (-9) over the Run (6), or (-9/6). The slope of this line is - 1.5.

We now have y = -1.5x + b. To find b, use wither of the two points. I'll use (2,-6) because I like even numbers, but fell free to use the other. Both will give the same answer for b. [Try it].

Using (2,-6), we get:

y = -1.5x + b

-6 = -1.5*(2) + b

-6 = -3 + b

b = -3

The equation is y = -1.5x - 3

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For fun, try the other point, (-4,3) to find the value of b:

y = -1.5x + b

3 = -1.5*(-4) + b

3 = 6 + b

b = -3 The Same!