Change the statement from standard form to slope-intercept form. Identify the slope and

Question

y-intercept.
4x+7y<14

Answer 1

To convert the inequality \(4x + 7y < 14\) from standard form to slope-intercept form (which is \(y = mx + b\)), follow these steps:

1. Isolate \(y\) on one side of the inequality:

   \[ 7y < 14 - 4x \]

2. Divide each term by 7 to solve for \(y\):

   \[ y < \frac{14 - 4x}{7} \]

   This can be simplified as:

   \[ y < -\frac{4}{7}x + 2 \]

Now, we have the inequality in slope-intercept form where:

• The slope \(m = -\frac{4}{7}\)
• The y-intercept \(b = 2\)

So, the final result in slope-intercept form is:

\[ y < -\frac{4}{7}x + 2 \]

• Slope: \( -\frac{4}{7} \)
• Y-intercept: \( 2 \)