Find the equation in standard form which passes through (-2, -7) and (1, -1). You must show all work.

Question

Find the equation in standard form which passes through (-2, -7) and (1, -1). You must show all work.

Answer 1

You will need to find two things to answer this problem: the slope and the y-intercept.

 

The slope is found with the formula (y₂-y₁)/(x₂-x_1). Note it doesn't matter which point you pick, as long as you are consistent with your choice.

 

I will go with, (-1+7)/(1+2) = (6/3) = 2. Note that here, I subtracted -7 from -1, and -2 from 1; that is why you see the + signs.

 

The y-intercept is quite simple. Since this is the point where the x-value = 0, to find it, just plug in 0 into the x-value (in the equation for a line) and see what you get. However, we don't have an equation for this line completed. So we start with the standard: y=mx + b.

 

y = y-value

x = x-value

m= slope

b= y-intercept

 

Note that we have found the slope! Also, we have x and y values given to us already (we can use -2,-7, or we can use 1,-1). This will let us estimate the equation for a line by finding the y-intercept.

 

Let us use (1, -1). What is that saying? Since this line passes through these points, it is saying, when x is 1, y is somehow, -1. Lets try it:

 

-1 = 2(1) + b

-1 = 2 + b 

b = -3

 

Plug this back into the equation for a line, and you will end up with: y = 2x -3.