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

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

$y = mx + b$

Where,

m: slope of the line

b: cutting point with the y axis.

For the slope of the line we have:

$m=\frac{y2-y1}{x2-x1}$

Substituting values we have:

$m=\frac{-4-8}{-6-4}$

Rewriting we have:

$m=\frac{-12}{-10}$

$m=\frac{6}{5}$

Then, we choose an ordered pair:

$(xo, yo) = (4, 8)$

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

$y-yo = m (x-xo)$

$y-8 = \frac{6}{5} (x-4)$

Rewriting we have:

$y = \frac{6}{5}x -\frac{24}{5} + 8$

$y = \frac{6}{5}x -\frac{24}{5} + \frac{40}{5}$

$y = \frac{6}{5}x + \frac{16}{5}$

Answer:

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

$y = \frac{6}{5}x + \frac{16}{5}$

Answer 2

Answer:

y = $\frac{6}{5} x + \frac{16}{5}$

Step-by-step 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) = $\frac{y2 - y1}{x2 - x1}$

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

Plug in these values in the above formula, we get

slope(m) = $\frac{8 - (-4)}{4 -(-6)}$

= $\frac{12}{10}$

Slope (m) = $\frac{6}{5}$

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 +($\frac{(36 - 20)}{5}$

y = $\frac{6}{5} x + \frac{16}{5}$