Question

The endpoints of GE are located at G(–6, –4) and E(4, 8). Using slope-intercept form, write the equation of GE.

Answer 1

y =
`(6)/(5) x + (16)/(5)`

Explanation:

The slope-intercept form is y = mx + b, where "m" is the slope and 'b" is the y-intercept.

Given: G(-6, -4) and E(4, 8)

Now we can use these points G(-6, -4) and E(4, 8) and find the slope.

Slope (m) =
`(y2 - y1)/(x2 - x1)`

Here x1 = -6, y1 = -4, x2 = 4 and y2 = 8

Plug in these values in the above formula, we get

slope(m) =
`(8 - (-4))/(4 -(-6))`

=
`(12)/(10)`

Slope (m) =
`(6)/(5)`

Now we can use the formula (y - y1) = m(x - x1) and find the required equation.

We can plug in m value and (x1, y1) value and find the equation.

y - (-4) = 6/5(x - (-6))

y + 4 = 6/5(x + 6)

Using the distributive property a(b + c) = ab + ac, we get

y + 4 = 6/5 x + 36/5

y = 6/5 x + 36/5 - 4

y =6/5 x +(
`((36 - 20))/(5)`

y =
`(6)/(5) x + (16)/(5)`

Answer 2

The equation of the line in slope-intercept form is:

`image`

Where,

m: slope of the line

b: cutting point with the y axis.

For the slope of the line we have:

`m=(y2-y1)/(x2-x1)`

Substituting values we have:

`m=(-4-8)/(-6-4)`

Rewriting we have:

`m=(-12)/(-10)`

`m=(6)/(5)`

Then, we choose an ordered pair:

`image`

Substituting values in the generic equation of the line we have:

`image`

`y-8 = (6)/(5) (x-4)`

Rewriting we have:

`y = (6)/(5)x -(24)/(5) + 8`

`y = (6)/(5)x -(24)/(5) + (40)/(5)`

`y = (6)/(5)x + (16)/(5)`

Answer:

The equation of the line in slope-intercept form is:

`y = (6)/(5)x + (16)/(5)`