Question

What is the y-intercept of the line that passes through the points (3,5) and(-4,-9)? *

Answer 1

The y-intercept is -1

Step-by-step explanation

First we have to find the slope of the line and then find the y-intercept from the slope-intercept form of its equation:

`y=mx+b`

m is the slope and b is the y-intercept.

The slope of a line that passes through points (x1, y1) and (x2, y2) is:

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

For this line, the slope is:

`m=(5-(-9))/(3-(-4))=(5+9)/(3+4)=(14)/(7)=2`

For now we have:

`y=2x+b`

To find the y-intercept, b, we have to replace x and y with the coordinates of one of the given points and solve for b:

`\begin{gathered} 5=2\cdot3+b \\ 5=6+b \\ b=5-6 \\ b=-1 \end{gathered}`