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

To find the equation of line segment GE with endpoints G(–6, –4) and E(4, 8), you calculate the slope, use one point to find the y-intercept, and then use these to write the equation in slope-intercept form, which is y = 1.2x + 3.2.

Step-by-step explanation:

To write the equation of line segment GE with endpoints G(–6, –4) and E(4, 8), we first need to calculate the slope (m) of the line. The slope is determined by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the given points G and E into the formula gives us m = (8 - (-4)) / (4 - (-6)) = 12 / 10 = 1.2.

Now that we have the slope, we can use one of the points and the slope to find the y-intercept (b) using the point-slope form equation, y - y1 = m(x - x1). Let's use point G for this: y - (-4) = 1.2(x - (-6)), simplifying this we get y + 4 = 1.2x + 7.2. Therefore, the y-intercept b = 7.2 - 4 = 3.2.

Finally, the equation of the line in slope-intercept form (y = mx + b) is y = 1.2x + 3.2. This is the equation that represents the line segment GE.

Answer 2

Answer:
Equation of the line is:
y = 1.2x + 3.2

Step-by-step explanation:
The general form of the linear equation is:
y = mx + c
where:
m is the slope
c is the y-intercept

1- getting the slope:
The slope of the line can be calculated using the following formula:
m =
`(y2 - y1)/(x2 - x1)`

We are given the points:
(-6,-4) representing (x1,y1)
(4,8) representing (x2,y2)
Substitute with the given points in the above equation to get the slope as follows:
m =
`(8--4)/(4--6) = 6/5`

The equation of the line now is:
y = 1.2x + c

2- getting the y-intercept:
To get the value of the c, we will use any of the given points, substitute in the equation and solve for c.
I will use the point (4,8) as follows:
y = 1.2 x + c
8 = 1.2(4) + c
c = 16/5 = 3.2

Therefore, the equation of the line is:
y = 1.2x + 3.2

Hope this helps :)