Question

A line passes through the points 1,-6 and 4,3what is the y-intercept of this line

Answer 1

To find the y-intercept we can find the "slope-intercept" equation for the line. This equation is given by the following expression:

`y=m\cdot x+b`

Where "m" is the slope and "b" is the y-intercept. We can find the slope by using:

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

Where (x1, y1) and (x2, y2) are two points that belong to the line. In this case we have (1, -6) and (4, 3) to apply on the equation.

`m=(3-(-6))/(4-1)=(9)/(3)=3`

We have the equation:

`y=3\cdot x+b`

To find the y-intercept we can use either point as shown below:

`\begin{gathered} 3=3\cdot4_{}+b \\ 3=12+b \\ b=3-12 \\ b=-9 \end{gathered}`

The y-intercept of the line is -9.