#23 ### Question**What is the slope of the line \(4x + 6y = 12\)?**#### Multiple Choices:1. \(\quad \circ \quad -\frac{2}{3} \)2. \(\quad \circ \quad 2 \)3. \(\quad \circ \quad \frac{2}{3} \)4. \(\quad \circ \quad 6 \)---#### Explanation of the Diagram- The diagram presented above is a multiple-choice question.- The question is asking for the slope of the line represented by the equation \(4x + 6y = 12\).- There are four multiple-choice options available for selection. Each option is denoted by a circle, which can be filled to indicate a chosen answer.---### SolutionTo determine the slope of the line given by the equation \(4x + 6y = 12\):1. **Convert the equation to slope-intercept form ( \(y = mx + b\) ):** - Start with the given equation: \(4x + 6y = 12\). - Solve for \(y\): \[ 6y = -4x + 12 \] \[ y = -\frac{4}{6}x + \frac{12}{6} \] \[ y = -\frac{2}{3}x + 2 \] - The slope-intercept form of the line is \(y = -\frac{2}{3}x + 2\).2. **Identify the slope ( \(m\) ):** - By comparing \(y = -\frac{2}{3}x + 2\) with \(y = mx + b\), we observe that the slope \(m = -\frac{2}{3}\).Therefore, the correct answer is: \(\quad \circ \quad -\frac{2}{3} \)---This explanation will help learners understand how to derive the slope of a line from a linear equation by converting it to slope-intercept form.

Name: #23 ### Question**What is the slope of the line \(4x + 6y = 12\)?**###
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: #23 ### Question**What is the slope of the line \(4x + 6y = 12\)?**#### Multiple Choices:1. \(\quad \circ \quad -\frac{2}{3} \)2. \(\quad \circ \quad 2 \)3. \(\quad \circ \quad \frac{2}{3} \)4. \(\quad \circ \quad 6 \)---#### Explanation of the Diagr