https://file.aiquickdraw.com/mathbot/file/1729505840329lywxsff2.jpg

You have provided a set of linear equations that need to be graphed using intercepts. Here's a step-by-step guide for solving these problems.

### General Method for Finding Intercepts:
1. **X-Intercept**: Set \( y = 0 \) and solve for \( x \).
2. **Y-Intercept**: Set \( x = 0 \) and solve for \( y \).

Let me walk through one of the exercises and guide you on the others.

#### Example: Problem 45
The equation is:
\[
-x + 4y = 8
\]

- **X-Intercept**: Set \( y = 0 \):
\[
-x = 8 \quad \Rightarrow \quad x = -8
\]
So, the x-intercept is \( (-8, 0) \).

- **Y-Intercept**: Set \( x = 0 \):
\[
4y = 8 \quad \Rightarrow \quad y = 2
\]
So, the y-intercept is \( (0, 2) \).

These points \( (-8, 0) \) and \( (0, 2) \) are enough to graph the line.

Would you like me to help solve specific exercises or provide further explanations for others? Let me know which one you'd like next, or if you'd like to work on a particular graph!

### Here are some related questions to explore:
1. How do you find intercepts for more complex equations like \( 2x - 5y = -20 \)?
2. How does the slope of the line affect the steepness of the graph?
3. What is the geometric significance of a positive vs. negative slope?
4. How would you graph horizontal or vertical lines, like \( y = -1 \) or \( x = 3 \)?
5. How do different forms of linear equations (slope-intercept form vs. standard form) impact the graphing method?

**Tip**: Always use the intercepts method when the equation is in standard form \( Ax + By = C \), as it simplifies graphing.

Graph a line using intercepts for various linear equations like -x + 4y = 8, x - y = -4, and more.

Learn how to graph linear equations using intercepts with exercises such as -x + 4y = 8 and x - y = -4. This tutorial covers essential algebraic concepts and step-by-step solutions, suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation