Question

Write the equation of the line that passes through the points (3,-8) and (-8, 1).

Answer 1

Answer:In order to write an equation for a line when we are only given 2 points it passes through, we first need to determine the slope of the line. The slope of the line is found by dividing the difference in the y-coordinates of the 2 points by the difference in the x-coordinates of the 2 points. (mathematically known as rise over run), (you may remember hearing this in class)

Step-by-step explanation:

y1-y2  / x1-x2 is the formula we will use to find the slope.

Pick one of the coordinates to be 1 and let the other be 2. We will let (3, 8) be 1 and (1, 0) be 2 because it has a 0 and subtracting 0 is easier.

Remember - whichever point contains y1, must also contain x1.

Our slope is found by substituting

(8 - 0) / (3 - 1) =

8 / 2 = 4. So the slope is 4.

Our equation for the line must be in the form of

y = mx + b (m is the slope and be is the y-intercept, where the line crosses the y-axis)

Again, choose a point and we will finish the equation. Let's use (1, 0). Always easier to use when there is a 0.

We will substitute our coordinates into the equation -

y - y1 = m(x - x1)

y - 0 = 4(x - 1)

y = 4x - 4 - your equation.

You can check your work by using the other point, (3, 8)

y = 4x - 4

8 = 4(3) - 4

8 = 12 - 4

Because this equation is true, your equation for the line is correct.

Hope this helps.