Help me with all of them please. ---### 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{

Name: Help me with all of them please. ---### Finding Intercepts and Graphin
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Description: Help me with all of them please. ---### 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\

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Math

Algebra

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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Help me with all of them please.

---

### 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{

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