Question

Find the x- and y-intercepts of the line 5x + 17y = -25

and

Find the x- and y-intercepts of the line 6x - 7y = -21

Answer 1

(0, -25/17)

Explanation:

To find the x-intercept of a line, we need to set y equal to zero and solve for x. To find the y-intercept, we need to set x equal to zero and solve for y.

For the line 5x + 17y = -25, setting y equal to zero gives us:

5x + 17(0) = -25

5x = -25

x = -5

Thus, the x-intercept is (-5, 0).

Setting x equal to zero gives us:

5(0) + 17y = -25

17y = -25

y = -25/17

Thus, the y-intercept is (0, -25/17).

Therefore, the x-intercept is (-5, 0) and the y-intercept is (0, -25/17).

Answer 2

To find the x- and y-intercepts of a line, we can set either the x-coordinate or the y-coordinate to 0 and solve for the other coordinate.

For the first line, 5x + 17y = -25, we can find the x-intercept by setting y = 0:

5x + 17(0) = -25

5x = -25

x = -5

Therefore, the x-intercept of the line 5x + 17y = -25 is (-5, 0).

To find the y-intercept, we can set x = 0:

5(0) + 17y = -25

17y = -25

y = -25 / 17

y = -1.47

Therefore, the y-intercept of the line 5x + 17y = -25 is (0, -1.47).

For the second line, 6x - 7y = -21, we can find the x-intercept by setting y = 0:

6x - 7(0) = -21

6x = -21

x = -21 / 6

x = -3.5

Therefore, the x-intercept of the line 6x - 7y = -21 is (-3.5, 0).

To find the y-intercept, we can set x = 0:

6(0) - 7y = -21

-7y = -21

y = 21 / -7

y = -3

Therefore, the y-intercept of the line 6x - 7y = -21 is (0, -3).