Question

35. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.

35. Passes through (-2, 8) and (4, 6)

Answer 1

The linear equation for the line which passes through the points given as (-2,8) and $(4,6), is written in the point-slope form as
`$y=-(1)/(3) x-(26)/(3)$`.

Explanation:

A condition is given that a line passes through the points whose coordinates are (-2,8) and (4,6).

It is asked to find the linear equation which satisfies the given condition.

Step 1 of 3

Determine the slope of the line.

The points through which the line passes are given as (-2,8) and (4,6). Next, the formula for the slope is given as,

`$m=(y_(2)-y_(1))/(x_(2)-x_(1))$`

Substitute
`$6 \& 8$` for
`$y_(2)$` and
`$y_(1)$` respectively, and 4&-2 for
`$x_(2)$` and
`$x_(1)$` respectively in the above formula. Then simplify to get the slope as follows,
`$m=(6-8)/(4-(-2))$`

`$$\begin{aligned}&m=(-2)/(6) \\&m=-(1)/(3)\end{aligned}$$`

Step 2 of 3

Write the linear equation in point-slope form.

A linear equation in point slope form is given as,

`$y-y_(1)=m\left(x-x_(1)\right)$`

Substitute
`$-(1)/(3)$` for m,-2 for
`$x_(1)$`, and 8 for
`$y_(1)$` in the above equation and simplify using the distributive property as follows,
`y-8=-(1)/(3)(x-(-2))$\\ $y-8=-(1)/(3)(x+2)$\\ $y-8=-(1)/(3) x-(2)/(3)$`

Step 3 of 3

Simplify the equation further.

Add 8 on each side of the equation
`$y-8=-(1)/(3) x-(2)/(3)$`, and simplify as follows,
`$y-8+8=-(1)/(3) x-(2)/(3)+8$`

`$y=-(1)/(3) x-(2+24)/(3)$$\\ $$y=-(1)/(3) x-(26)/(3)$$`

This is the required linear equation.