- Linear Functions and
Question 15, 2.3.61
Part 1 of 3
a. Rewrite the given equation $3 x+8 y-24=0$ slope-intercept form.
b. Give the slope and $y$-intercept.
c. Use the slope and $y$-intercept to graph the linear function.
a. The slope-intercept form of the equation is
(Simplify your answer. Use integers or fractions for any numbers in the equation.)

Step 1 ：Rewrite the given equation \(3x + 8y - 24 = 0\) in slope-intercept form by isolating \(y\).

Step 2 ：Subtract \(3x\) from both sides to get \(8y = -3x + 24\).

Step 3 ：Divide every term by \(8\) to solve for \(y\), yielding \(y = -\frac{3}{8}x + 3\).

Step 4 ：From the equation \(y = -\frac{3}{8}x + 3\), identify the slope \(m\) as \(-\frac{3}{8}\) and the y-intercept \(b\) as \(3\).

Step 5 ：To graph the linear function, start by plotting the y-intercept \((0, 3)\).

Step 6 ：Since the slope is \(-\frac{3}{8}\), move down 3 units and to the right 8 units from the y-intercept to plot another point.

Step 7 ：Draw a line through these two points to represent the linear function.