Find the​ x- and​ y-intercepts of the line that passes through the given points.

Question

(-5, -5,), (5,-1)

The​ x-intercept is 15/2
The​ y-intercept is
​(Type an integer or a​ fraction.)

Answer 1

To find the x-intercept, we need to find the value of x when y = 0.

The equation of the line passing through the two given points can be found using the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope (m). The slope is calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
m = (-1 - (-5)) / (5 - (-5))
m = (4) / (5 + 5)
m = 4 / 10
m = 2/5

Now, substitute the slope and the coordinates of one of the points (5, -1) into the slope-intercept form equation:
-1 = (2/5)(5) + b

Solve for b:
-1 = 2 + b
b = -3

So, the equation of the line passing through the two points is: y = (2/5)x - 3.

To find the x-intercept, substitute y = 0 into the equation:
0 = (2/5)x - 3

Solve for x:
(2/5)x = 3
2x = 3 * 5
2x = 15
x = 15/2

Therefore, the x-intercept of the line is 15/2.

To find the y-intercept, substitute x = 0 into the equation:
y = (2/5)*0 - 3
y = -3

Therefore, the y-intercept of the line is -3.