https://file.aiquickdraw.com/mathbot/file/1727045456401il6tsjr2.jpg

We are given the equation:

\[
4 - 5y = -26 - 3x
\]

### Step 1: Find the x-intercept
The x-intercept occurs when \( y = 0 \). Let's substitute \( y = 0 \) into the equation:

\[
4 - 5(0) = -26 - 3x
\]

Simplifying this:

\[
4 = -26 - 3x
\]

Now, solve for \( x \):

\[
4 + 26 = -3x
\]
\[
30 = -3x
\]
\[
x = \frac{30}{-3} = -10
\]

Thus, the x-intercept is \( (-10, 0) \).

### Step 2: Find the y-intercept
The y-intercept occurs when \( x = 0 \). Let's substitute \( x = 0 \) into the equation:

\[
4 - 5y = -26 - 3(0)
\]

Simplifying this:

\[
4 - 5y = -26
\]

Now, solve for \( y \):

\[
4 + 26 = 5y
\]
\[
30 = 5y
\]
\[
y = \frac{30}{5} = 6
\]

Thus, the y-intercept is \( (0, 6) \).

### Final Result
- x-intercept: \( (-10, 0) \)
- y-intercept: \( (0, 6) \)

Would you like further details or explanations on this? Let me know if you have any questions.

Here are 5 related questions to explore further:
1. How do we graph a line using intercepts?
2. How do we convert this equation to slope-intercept form?
3. Can you explain the relationship between intercepts and the slope of a line?
4. What happens if an equation has no x- or y-intercept?
5. How do we solve systems of equations graphically using intercepts?

**Tip:** When finding intercepts, always substitute one variable as zero to isolate the other.

Consider the following equation: 4 - 5y = -26 - 3x. Find the x- and y-intercepts, if possible.

Learn how to find the x- and y-intercepts of the linear equation 4 - 5y = -26 - 3x. Step-by-step explanation includes setting y = 0 to find the x-intercept and x = 0 to find the y-intercept. Suitable for students in 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