Question

A line passes through the points (5, –7.5) and has a y-intercept 10.

Which is a linear function in the form of y = mx + b for this line?

Answer 1

y= -3.5x +10

Explanation:

The first thing to do in this equation is solve for m, the slope of the line.

Because we are given that the y-intercept is 10, we know that the graph intercepts at the point (0,10).

We are also given the point (5,-7.5).

Using the two points we can solve for the slope!

To solve for the slope use this formula:
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

(-7.5 -10) / (5 -0)

= -3.5

So our slope, m = -3.5

The other missing value is b, but is very easy to find.

In this example, b is equal to the y-intercept, so b=10.

Now we can plug in the values we found into the original equation

y =mx+b

y= -3.5x +10