Graph 3x = -5y + 8 by finding the intercepts. We will let x = 0 to find the y-intercept of the graph. We will then let y = 0 to find the x-intercept. Since two points determine a line, the y-intercept and x-intercept are enough information to graph this linear equation. We find the intercepts and select x = 1 to find a check point. Check point: x = 1 3x = -5y + 8 y-intercept: x = 0 x-intercept: y = 0 Зх %3D —5у + 8 3x = -5( ) + 8 Зх %3D —5у + 8 -! 3( -5y + 8 3( = -5y + 8 0 = -5y + X = 8 3 = -5y + = -5y = -5y X = 3 = y = y A check point is (1, 1). X = 2 3 1 = y 5 (2를,이). The y-intercept is (0, 12). The x-intercept is The ordered pairs are plotted as shown, and a straight line is then drawn through them. y 3x = -5y + 8 2. Зх %3D —5у + 8 (1, 1) y (х, у) 8 13 4 -3 -2 = 0, 5 y-intercept 5 (2를이) -2 8 e x-intercept 3 -3 1 (1, 1) Check point N/3
Graph 3x = -5y + 8 by finding the intercepts. We will let x = 0 to find the y-intercept of the graph. We will then let y = 0 to find the x-intercept. Since two points determine a line, the y-intercept and x-intercept are enough information to graph this linear equation. We find the intercepts and select x = 1 to find a check point. Check point: x = 1 3x = -5y + 8 y-intercept: x = 0 x-intercept: y = 0 Зх %3D —5у + 8 3x = -5( ) + 8 Зх %3D —5у + 8 -! 3( -5y + 8 3( = -5y + 8 0 = -5y + X = 8 3 = -5y + = -5y = -5y X = 3 = y = y A check point is (1, 1). X = 2 3 1 = y 5 (2를,이). The y-intercept is (0, 12). The x-intercept is The ordered pairs are plotted as shown, and a straight line is then drawn through them. y 3x = -5y + 8 2. Зх %3D —5у + 8 (1, 1) y (х, у) 8 13 4 -3 -2 = 0, 5 y-intercept 5 (2를이) -2 8 e x-intercept 3 -3 1 (1, 1) Check point N/3
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![---
### Finding Intercepts and Graphing a Linear Equation
#### Objective:
Graph the linear equation \(2x = -2y + 16\) by finding the intercepts.
#### Steps to Find Intercepts:
1. **Find the y-intercept:**
- Set \(x = 0\) and solve for \(y\):
\[
2(0) = -2y + 16 \implies -2y + 16 = 0 \implies y = \frac{16}{2} \implies y = 8
\]
\[
\text{y-intercept is } (0, 8)
\]
2. **Find the x-intercept:**
- Set \(y = 0\) and solve for \(x\):
\[
2x = -2(0) + 16 \implies 2x = 16 \implies x = \frac{16}{2} \implies x = 8
\]
\[
\text{x-intercept is } (8, 0)
\]
3. **Check another point:**
- Choose another value for \(x\) or \(y\). For simplicity, set \(x = 4\):
\[
2(4) = -2y + 16 \implies 8 = -2y + 16 \implies -2y = 8 - 16 \implies y = \frac{-8}{-2} \implies y = 4
\]
\[
\text{Check point is } (4, 4)
\]
#### Graphical Representation:
- Using the table and the intercept points identified, plot the points on a coordinate graph. Connect the points to draw the line representing the equation \(2x = -2y + 16\).
#### Example Table:
| \( x \) | \( y \) | \( (x, y) \) |
|:-------:|:-------:|:----------:|
| 0 | 8 | \((0, 8)\) |
| 8 | 0 | \((8, 0)\) |
| 4 | 4 | \((4, 4)\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46673039-9c26-4fb7-977e-77e5eaa45b18%2F8016aa6a-76ae-4dff-8ddd-bb8b1007c4b0%2Fvk352o_processed.png&w=3840&q=75)
Transcribed Image Text:---
### Finding Intercepts and Graphing a Linear Equation
#### Objective:
Graph the linear equation \(2x = -2y + 16\) by finding the intercepts.
#### Steps to Find Intercepts:
1. **Find the y-intercept:**
- Set \(x = 0\) and solve for \(y\):
\[
2(0) = -2y + 16 \implies -2y + 16 = 0 \implies y = \frac{16}{2} \implies y = 8
\]
\[
\text{y-intercept is } (0, 8)
\]
2. **Find the x-intercept:**
- Set \(y = 0\) and solve for \(x\):
\[
2x = -2(0) + 16 \implies 2x = 16 \implies x = \frac{16}{2} \implies x = 8
\]
\[
\text{x-intercept is } (8, 0)
\]
3. **Check another point:**
- Choose another value for \(x\) or \(y\). For simplicity, set \(x = 4\):
\[
2(4) = -2y + 16 \implies 8 = -2y + 16 \implies -2y = 8 - 16 \implies y = \frac{-8}{-2} \implies y = 4
\]
\[
\text{Check point is } (4, 4)
\]
#### Graphical Representation:
- Using the table and the intercept points identified, plot the points on a coordinate graph. Connect the points to draw the line representing the equation \(2x = -2y + 16\).
#### Example Table:
| \( x \) | \( y \) | \( (x, y) \) |
|:-------:|:-------:|:----------:|
| 0 | 8 | \((0, 8)\) |
| 8 | 0 | \((8, 0)\) |
| 4 | 4 | \((4, 4)\)
![**Graphing the Equation 3x = -5y + 8 by Finding Intercepts**
**Objective:**
Learn how to graph the equation \(3x = -5y + 8\) by determining its intercepts.
**Steps:**
1. **Finding the y-intercept:**
To find the y-intercept, let \(x = 0\) and solve for \(y\):
\[ 3(0) = -5y + 8 \]
\[ 0 = -5y + 8 \]
\[ -5y = -8 \]
\[ y = \frac{8}{5} \]
Therefore, the y-intercept is \(\left(0, \frac{8}{5}\right)\) or \(\left(0, \frac{1}{3} \right)\).
2. **Finding the x-intercept:**
To find the x-intercept, let \(y = 0\) and solve for \(x\):
\[ 3x = -5(0) + 8 \]
\[ 3x = 8 \]
\[ x = \frac{8}{3} \]
Therefore, the x-intercept is \(\left(\frac{8}{3}, 0\right)\) or \(\left(\frac{2}{2}, 0 \right)\).
3. **Check point:**
Select \(x = 1\) to find a check point:
\[ 3(1) = -5y + 8 \]
\[ 3 = -5y + 8 \]
\[ -5y = 3 - 8 \]
\[ -5y = -5 \]
\[ y = 1 \]
A check point is (1, 1).
**Ordered Pairs and Graph:**
Using the intercepts and the check point, plot the ordered pairs on a graph.
**Table of Intercepts and Check Point:**
| \(x\) | \(y\) | \((x, y)\) |
|----------|----------|----------------------|
| 0 | \(\frac{8}{5}\) | \(\left(0, \frac{8}{5}\right)\) |
| \(\frac{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46673039-9c26-4fb7-977e-77e5eaa45b18%2F8016aa6a-76ae-4dff-8ddd-bb8b1007c4b0%2F98cox6u_processed.png&w=3840&q=75)
Transcribed Image Text:**Graphing the Equation 3x = -5y + 8 by Finding Intercepts**
**Objective:**
Learn how to graph the equation \(3x = -5y + 8\) by determining its intercepts.
**Steps:**
1. **Finding the y-intercept:**
To find the y-intercept, let \(x = 0\) and solve for \(y\):
\[ 3(0) = -5y + 8 \]
\[ 0 = -5y + 8 \]
\[ -5y = -8 \]
\[ y = \frac{8}{5} \]
Therefore, the y-intercept is \(\left(0, \frac{8}{5}\right)\) or \(\left(0, \frac{1}{3} \right)\).
2. **Finding the x-intercept:**
To find the x-intercept, let \(y = 0\) and solve for \(x\):
\[ 3x = -5(0) + 8 \]
\[ 3x = 8 \]
\[ x = \frac{8}{3} \]
Therefore, the x-intercept is \(\left(\frac{8}{3}, 0\right)\) or \(\left(\frac{2}{2}, 0 \right)\).
3. **Check point:**
Select \(x = 1\) to find a check point:
\[ 3(1) = -5y + 8 \]
\[ 3 = -5y + 8 \]
\[ -5y = 3 - 8 \]
\[ -5y = -5 \]
\[ y = 1 \]
A check point is (1, 1).
**Ordered Pairs and Graph:**
Using the intercepts and the check point, plot the ordered pairs on a graph.
**Table of Intercepts and Check Point:**
| \(x\) | \(y\) | \((x, y)\) |
|----------|----------|----------------------|
| 0 | \(\frac{8}{5}\) | \(\left(0, \frac{8}{5}\right)\) |
| \(\frac{
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