Question

Which equation represents the line that passes through the points (3, 4) and (1, - 2)? Select one: 1) y = 3x - 5 2) y=x+1 3) y = - 3x + 13 4) y = -x +7

Answer 1

To find the equation of a line you need to know the slope (m) and the y-intercept (b):

`y=mx+b`

With the given points (x,y) you can calculate the slope using the next formula:

`m=((y_2-y_1))/((x_2-x_1))`

(3,4) x1= 3 y1= 4

(1, -2) x2=1 y2= -2

`m=(-2-4)/(1-3)=(-6)/(-2)=3`m= 3

You use one of the given points (x,y) to find the y-intercept as follow:

(3,4) x= 3 y= 4

`\begin{gathered} y=mx+b \\ 4=3(3)+b \\ 4=9+b \\ 4-9=b \\ -5=b \end{gathered}`b= -5

Then, the equation of the line that passes through the points (3, 4) and (1, - 2) is:

`y=3x-5`