A line passes through the points (5,-7.5) and has a y-intercept 10. How can i write the linear function in the form y=mx+b???

Question

I already know how to find the y-intercept using slope but I am so confused with this one because they already gave me a y-intercept, y1 and y2 but how can I do the slope If I dont have a x1 and x2?

Answer 1

Hello, Rhymie!

This is not as difficult as it seems. :)

First, let's look at the equation y = mx + b. This is the slope-intercept form of a line, where m is the slope and b is the y-intercept(the place where the line intercepts the y- axis).

Since you already are given the y-intercept (b), then you just need to substitute the point (5, -7.5) for the x and y in the equation and you can then find the slope (m).

So, y = mx + b

is now y = mx + 10.

Now substitute (5,-7.5) for (x,y) in the equation.

-7.5 = m(5) + 10

-7.5 = 5m + 10

-17.5 = 5m

m = -17.5/5 = -3.5

So now we can find the equation of the line that passes through the points (5, -7.5) with y - intercept 10:

y = -3.5x + 10