Question

Write the equation of the line that passes through the given points. (0,-5) and (8,0)​

Answer 1

`y=(5)/(8)x-5`

Explanation:

You're given two points, using that you can use the slope-finding formula:

`slope=((y^(2) - y^(1)) )/((x^(2) - x^(1)))`

After that, match up the y-coordinates with each other and the same goes for the x-coordinates. It should look something like this:

`slope = ((0-(-5)))/((8-0)) \\\\=(5)/(8)`

5/8 is your slope. Using the general slope formula y=mx + b, you know that m is the slope and b is the y-intercept. So now you know your slope, plug it into the formula, along with one of the given points. In this case, I will be using (8, 0) because it is easier to solve.

`m = (5)/(8)\\ \\y = ((5)/(8) )x+b\\(8, 0)\\(0) = (5)/(8)(8) + b\\ 0 = 5 + b\\\\-5 =b\\ \\y=(5)/(8)x-5`

You can see I replaced the x and y with the given values accordingly. Then you simplify by subtracting the five on both sides and your y-intercept is -5. Then combine your slope and y-intercept to get your answer!

Hope that helped!

-Bob Ross