Question

What is the y-intercept of a line that passes through the points (1-7) and (5-25)?

Answer 1

Given:

A line passes through the points (1,-7) and (5,-25).

To find:

The y-intercept of the line.

Solution:

The line passes through the points (1-7) and (5-25). So, the equation of the line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

`y-(-7)=(-25-(-7))/(5-1)(x-1)`

`y+7=(-25+7)/(4)(x-1)`

`y+7=(-18)/(4)(x-1)`

`y+7=-4.5(x-1)`

Subtracting 7 from both sides, we get

`y=-4.5x+4.5-7`

`y=-4.5x-2.5`

Putting x=0, we get

`y=-4.5(0)-2.5`

`y=0-2.5`

`y=-2.5`

Therefore, the y-intercept of the given line is -2.5 and the vertex form of (0,-2.5).