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.