Math Snap

STEP 1

1. The $x$-intercept of a line is the point where the line crosses the $x$-axis, which occurs when $y = 0$.
2. The $y$-intercept of a line is the point where the line crosses the $y$-axis, which occurs when $x = 0$.
3. Each line equation can be solved separately for its intercepts.

STEP 2

1. Find the $x$-intercept for each line.
2. Find the $y$-intercept for each line.

STEP 3

For the line $2x + 3y = 24$, find the $x$-intercept by setting $y = 0$:
$$2x + 3(0) = 24$$ $$2x = 24$$ $$x = \frac{24}{2} = 12$$ The $x$-intercept is $(12, 0)$.

STEP 4

For the line $2x + 3y = 24$, find the $y$-intercept by setting $x = 0$:
$$2(0) + 3y = 24$$ $$3y = 24$$ $$y = \frac{24}{3} = 8$$ The $y$-intercept is $(0, 8)$.

STEP 5

For the line $3x - 5y = 30$, find the $x$-intercept by setting $y = 0$:
$$3x - 5(0) = 30$$ $$3x = 30$$ $$x = \frac{30}{3} = 10$$ The $x$-intercept is $(10, 0)$.

STEP 6

For the line $3x - 5y = 30$, find the $y$-intercept by setting $x = 0$:
$$3(0) - 5y = 30$$ $$-5y = 30$$ $$y = \frac{30}{-5} = -6$$ The $y$-intercept is $(0, -6)$.

STEP 7

For the line $7x - 4y = 84$, find the $x$-intercept by setting $y = 0$:
$$7x - 4(0) = 84$$ $$7x = 84$$ $$x = \frac{84}{7} = 12$$ The $x$-intercept is $(12, 0)$.

STEP 8

For the line $7x - 4y = 84$, find the $y$-intercept by setting $x = 0$:
$$7(0) - 4y = 84$$ $$-4y = 84$$ $$y = \frac{84}{-4} = -21$$ The $y$-intercept is $(0, -21)$.

STEP 9

For the line $x + y = 8$, find the $x$-intercept by setting $y = 0$:
$$x + 0 = 8$$ $$x = 8$$ The $x$-intercept is $(8, 0)$.

STEP 10

For the line $x + y = 8$, find the $y$-intercept by setting $x = 0$:
$$0 + y = 8$$ $$y = 8$$ The $y$-intercept is $(0, 8)$.

STEP 11

For the line $x = 5$, find the $x$-intercept. Since $x$ is always 5, the line is vertical and does not cross the $x$-axis at any other point. Thus, there is no $x$-intercept other than the point itself, which is $(5, 0)$.

STEP 12

For the line $x = 5$, find the $y$-intercept. Since the line is vertical, it does not cross the $y$-axis. Therefore, there is no $y$-intercept.

STEP 13

For the line $3y = 66$, find the $x$-intercept. Since $y$ is always a constant value, the line is horizontal and does not cross the $x$-axis. Therefore, there is no $x$-intercept.

For the line $3y = 66$, find the $y$-intercept by setting $x = 0$:
$$3y = 66$$ $$y = \frac{66}{3} = 22$$ The $y$-intercept is $(0, 22)$.