Question

Find the distance of the line, then find the slope of the line using the following coordinates (-7,2) and (-4,6)?

Answer 1

Distance = 5 units

Slope =
`\displaystyle(4)/(3)`

Explanation:

Hi there!

1) Finding the distance of the line

`d=√((x_2-x_1)^2+(y_2-y_1)^2)` where two endpoints of a line are
`(x_1,y_1)` and
`(x_2,y_2)`

Plug in the points (-7,2) and (-4,6):

`d=√((-4-(-7))^2+(6-2)^2)\\d=√((-4+7)^2+(6-2)^2)\\d=√((3)^2+(4)^2)\\d=√(9+16)\\d=√(25)\\d=5`

Therefore, the length of the line/distance of the line is 5 units.

2) Finding the slope of the line

`m=\displaystyle(y_2-y_1)/(x_2-x_1)` where two points are
`(x_1,y_1)` and
`(x_2,y_2)`

Plug in the points (-7,2) and (-4,6):

`m=\displaystyle(6-2)/(-4-(-7))\\\\m=\displaystyle(6-2)/(-4+7)\\\\m=\displaystyle(4)/(3)`

Therefore, the slope of the line is
`\displaystyle(4)/(3)`.

I hope this helps!