Linear functions

Question

write an equation that represents a line that passes through points (−6, 4) and (2, 0).

Answer 1

Hello Q,

There are several different ways of writing this equation. Remember an equation is something that is equal on both sides and will work for all x and all y. So you can test your equation with any x and any y.

The easiest equation to use is

y = mx + b

y = y

x= x

m = Slope (the rise over run of a line. Or how much does the line go up or down based on how much you move left or right)

b = Y intercept (what is the value of Y, when X = 0)

The equation for slope (m) is m = (y2-y1) / (x2-x1) = (0-4) / (2 - -6) = -4 / 8 = -1/2

Now to find the intercept. So right now our equation looks like:

y = -1/2 x + b

Remember an equation has to work for every point in that line, so we can plug in either point and solve for b. In this case, we will use (2,0)

0 = -1/2 (2) + b

0 = -1 + b

1 = b

So our y intercept is b, plug this back into our slope-intercept question and we get:

y = -1/2 x + 1

Hope this helps, please let me know if anything is unclear.