Question

use intercepts to graph the equation.
4x - 6y + 24 = 0

use the graphing tool to graph the line. use the intercepts when drawing the line. if only one intercept exists, use it and another point to draw the line.
click to enlarge graph

Explanation:

Step1: Find x-intercept (set y=0)

Substitute $y=0$ into $4x - 6y + 24 = 0$:
$$4x - 6(0) + 24 = 0$$
$$4x + 24 = 0$$
$$4x = -24$$
$$x = -6$$
x-intercept: $(-6, 0)$

Step2: Find y-intercept (set x=0)

Substitute $x=0$ into $4x - 6y + 24 = 0$:
$$4(0) - 6y + 24 = 0$$
$$-6y + 24 = 0$$
$$-6y = -24$$
$$y = 4$$
y-intercept: $(0, 4)$

Step3: Plot intercepts and draw line

Mark points $(-6, 0)$ and $(0, 4)$ on the grid, then draw a straight line through them.

Answer:

The line passes through the x-intercept $(-6, 0)$ and y-intercept $(0, 4)$; connecting these two points gives the graph of $4x - 6y + 24 = 0$.