Graph The Equation: $y + 2 = -\frac{3}{4}(x + 4$\]Complete The Table:$\[ \begin{tabular}{|l|l|} \hline $x$ & $y$ \\ \hline & \\ & \\ & \\ \hline \end{tabular} \\]Click Or Tap The Graph To Plot A Point.

Introduction

Graphing equations is a fundamental concept in mathematics, and it's essential to understand how to graph various types of equations. In this article, we will focus on graphing the equation $y + 2 = -\frac{3}{4}(x + 4)$. We will break down the process into manageable steps and provide a step-by-step guide on how to graph the equation.

Understanding the Equation

Before we start graphing the equation, let's understand what the equation represents. The equation $y + 2 = -\frac{3}{4}(x + 4)$ is a linear equation in the slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

In this equation, the slope is $-\frac{3}{4}$, and the y-intercept is $-2$. The slope represents the rate of change of the equation, and the y-intercept represents the point where the equation intersects the y-axis.

Graphing the Equation

To graph the equation, we need to find the x and y values that satisfy the equation. We can do this by substituting different values of x into the equation and solving for y.

Let's start by finding the x and y values for the equation $y + 2 = -\frac{3}{4}(x + 4)$.

Finding the x and y Values

To find the x and y values, we can substitute different values of x into the equation and solve for y.

x	y
-4	-2
-3	-\frac{3}{4}(-3 + 4) + 2 = -\frac{3}{4} + 2 = \frac{5}{4}
-2	-\frac{3}{4}(-2 + 4) + 2 = -\frac{3}{4} + 2 = \frac{5}{4}
-1	-\frac{3}{4}(-1 + 4) + 2 = -\frac{3}{4} + 2 = \frac{5}{4}
0	-\frac{3}{4}(0 + 4) + 2 = -3 + 2 = -1
1	-\frac{3}{4}(1 + 4) + 2 = -\frac{15}{4} + 2 = -\frac{7}{4}
2	-\frac{3}{4}(2 + 4) + 2 = -\frac{18}{4} + 2 = -\frac{13}{4}
3	-\frac{3}{4}(3 + 4) + 2 = -\frac{21}{4} + 2 = -\frac{17}{4}
4	-\frac{3}{4}(4 + 4) + 2 = -\frac{24}{4} + 2 = -6

Plotting the Points

Now that we have the x and y values, we can plot the points on a coordinate plane.

Plotting the Points

To plot the points, we need to use a coordinate plane with x and y axes. We can plot the points by marking the x and y values on the axes and drawing a line through the points.

Here is the plot of the points:

x	y
-4	-2
-3	\frac{5}{4}
-2	\frac{5}{4}
-1	\frac{5}{4}
0	-1
1	-\frac{7}{4}
2	-\frac{13}{4}
3	-\frac{17}{4}
4	-6

Graphing the Equation

Now that we have plotted the points, we can graph the equation by drawing a line through the points.

Here is the graph of the equation:

Graph of the Equation

The graph of the equation $y + 2 = -\frac{3}{4}(x + 4)$ is a straight line with a slope of $-\frac{3}{4}$ and a y-intercept of $-2$.

Conclusion

Graphing equations is a fundamental concept in mathematics, and it's essential to understand how to graph various types of equations. In this article, we have graphed the equation $y + 2 = -\frac{3}{4}(x + 4)$ by finding the x and y values and plotting the points on a coordinate plane. We have also graphed the equation by drawing a line through the points.

Table of Values

Here is the table of values for the equation $y + 2 = -\frac{3}{4}(x + 4)$:

x	y
-4	-2
-3	\frac{5}{4}
-2	\frac{5}{4}
-1	\frac{5}{4}
0	-1
1	-\frac{7}{4}
2	-\frac{13}{4}
3	-\frac{17}{4}
4	-6

Graphing the Equation: A Step-by-Step Guide

Here is a step-by-step guide on how to graph the equation $y + 2 = -\frac{3}{4}(x + 4)$:

1. Find the x and y values by substituting different values of x into the equation and solving for y.
2. Plot the points on a coordinate plane by marking the x and y values on the axes.
3. Draw a line through the points to graph the equation.

Graph of the Equation: A Visual Representation

Here is a visual representation of the graph of the equation $y + 2 = -\frac{3}{4}(x + 4)$:

$$$$

Introduction

Graphing equations is a fundamental concept in mathematics, and it's essential to understand how to graph various types of equations. In this article, we will provide a Q&A guide on graphing the equation $y + 2 = -\frac{3}{4}(x + 4)$.

Q&A Guide

Q: What is the slope of the equation $y + 2 = -\frac{3}{4}(x + 4)$? A: The slope of the equation is $-\frac{3}{4}$.

Q: What is the y-intercept of the equation $y + 2 = -\frac{3}{4}(x + 4)$? A: The y-intercept of the equation is $-2$.

Q: How do I find the x and y values for the equation $y + 2 = -\frac{3}{4}(x + 4)$? A: To find the x and y values, substitute different values of x into the equation and solve for y.

Q: How do I plot the points on a coordinate plane? A: To plot the points, mark the x and y values on the axes and draw a line through the points.

Q: What is the graph of the equation $y + 2 = -\frac{3}{4}(x + 4)$? A: The graph of the equation is a straight line with a slope of $-\frac{3}{4}$ and a y-intercept of $-2$.

Q: How do I determine the slope and y-intercept of the equation $y + 2 = -\frac{3}{4}(x + 4)$? A: The slope and y-intercept can be determined by rewriting the equation in slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Q: What is the significance of the slope and y-intercept in graphing the equation $y + 2 = -\frac{3}{4}(x + 4)$? A: The slope and y-intercept are essential in graphing the equation as they determine the direction and position of the line.

Q: How do I use the graph of the equation $y + 2 = -\frac{3}{4}(x + 4)$ to solve problems? A: The graph of the equation can be used to solve problems by finding the x and y values that satisfy the equation.

Q: What are some common mistakes to avoid when graphing the equation $y + 2 = -\frac{3}{4}(x + 4)$? A: Some common mistakes to avoid when graphing the equation include:

• Not rewriting the equation in slope-intercept form
• Not plotting the points correctly
• Not drawing the line through the points correctly

Conclusion

Graphing equations is a fundamental concept in mathematics, and it's essential to understand how to graph various types of equations. In this article, we have provided a Q&A guide on graphing the equation $y + 2 = -\frac{3}{4}(x + 4)$. We hope that this guide has been helpful in understanding how to graph the equation and solve problems.

Graphing the Equation: A Step-by-Step Guide

Here is a step-by-step guide on how to graph the equation $y + 2 = -\frac{3}{4}(x + 4)$:

1. Find the x and y values by substituting different values of x into the equation and solving for y.
2. Plot the points on a coordinate plane by marking the x and y values on the axes.
3. Draw a line through the points to graph the equation.

Graph of the Equation: A Visual Representation

Here is a visual representation of the graph of the equation $y + 2 = -\frac{3}{4}(x + 4)$:

The graph of the equation is a straight line with a slope of $-\frac{3}{4}$ and a y-intercept of $-2$.