Question

for the equation given below, complete parts a and b.\
$3x + 8y = 24$\
\
a. rewrite the given equation in slope - intercept form by solving for $y$.\
the slope - intercept form of the equation is \\(\square\\).\
(type an equation. use integers or fractions for any numbers in the equation.)\
b. use the slope and y - intercept to graph the linear function.\
use the graphing tool to graph the line. use the slope and y - intercept when drawing the line.

Explanation:

Part a

Step1: Isolate the term with y

We start with the equation \( 3x + 8y = 24 \). Subtract \( 3x \) from both sides to get \( 8y=-3x + 24 \).

Step2: Solve for y

Divide every term by 8. So \( y=\frac{-3x}{8}+\frac{24}{8} \), which simplifies to \( y = -\frac{3}{8}x + 3 \).

1. Identify y - intercept: From the slope - intercept form \( y=-\frac{3}{8}x + 3 \), the y - intercept \( b = 3 \). So we plot the point \( (0,3) \) on the y - axis.
2. Identify slope: The slope \( m=-\frac{3}{8} \). The slope is \( \frac{\text{rise}}{\text{run}} \), so from the point \( (0,3) \), we move down 3 units (because the rise is - 3) and then move 8 units to the right (because the run is 8) to get the next point \( (8,0) \).
3. Draw the line: Connect the points \( (0,3) \) and \( (8,0) \) (and extend the line in both directions) to graph the linear function.

Answer:

\( y = -\frac{3}{8}x + 3 \)

Part b