- 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.)

Answer

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Answer

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

Steps

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

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

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.