Question

Find the solution to the inequality 4x - 3y > 12 and rewrite it in slope-intercept form.

Answer 1

To solve the inequality \( 4x - 3y > 12 \) and rewrite it in slope-intercept form, we will isolate \( y \) on one side of the inequality.

Starting with the inequality:

\[
4x - 3y > 12
\]

We can subtract \( 4x \) from both sides:

\[
-3y > 12 - 4x
\]

Next, we will multiply the entire inequality by \(-1\). Remember, when multiplying or dividing an inequality by a negative number, we must reverse the inequality sign:

\[
3y < -12 + 4x
\]

Now, let's rearrange it to emphasize the terms involving \( y \):

\[
3y < 4x - 12
\]

Now, we will divide each term by 3 to solve for \( y \):

\[
y < \frac{4}{3}x - 4
\]

This is now in slope-intercept form \( y = mx + b \), where the slope \( m = \frac{4}{3} \) and the y-intercept \( b = -4 \).

The final solution in slope-intercept form is:

\[
y < \frac{4}{3}x - 4
\]