Question

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

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

The​ x-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 is equal to zero. We can set up the equation of the line using the formula for the slope, which is:

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

Using the given points (-5, -5) and (5, -1), we can substitute the coordinates into the slope formula:

m = (-1 - (-5)) / (5 - (-5))
= (-1 + 5) / (5 + 5)
= 4 / 10
= 2/5

Now, let's use the slope-intercept form of the line to find the equation:

y - y1 = m(x - x1)

Using the point (5, -1):

y - (-1) = (2/5)(x - 5)
y + 1 = (2/5)(x - 5)
y + 1 = (2/5)x - 2
y = (2/5)x - 3

To find the ​x-intercept, we set y = 0 and solve for x:

0 = (2/5)x - 3
(2/5)x = 3
2x = 15
x = 15/2

Therefore, the ​x-intercept is 15/2 or 7.5.