https://file.aiquickdraw.com/mathbot/file/1727057975331ki1m4kfw.jpg

Let's go through each problem from the image step by step:

### a. Solve: \( 4x - 5 = -5 \)

To solve for \( x \), add 5 to both sides:

\[
4x - 5 + 5 = -5 + 5
\]

\[
4x = 0
\]

Now, divide both sides by 4:

\[
x = \frac{0}{4} = 0
\]

So, \( x = 0 \).

---

### b. Find the \( x \)-intercept: \( 4x - 5y = -5 \)

The \( x \)-intercept occurs when \( y = 0 \). Substitute \( y = 0 \) into the equation:

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

\[
4x = -5
\]

Now, divide both sides by 4:

\[
x = \frac{-5}{4}
\]

So, the \( x \)-intercept is \( x = -\frac{5}{4} \) or \( -1.25 \).

---

### c. Find \( y \) when \( x = 0 \): \( 4x - 5y = -5 \)

Substitute \( x = 0 \) into the equation:

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

\[
-5y = -5
\]

Now, divide both sides by \( -5 \):

\[
y = 1
\]

So, \( y = 1 \).

---

### d. Solve for \( y \): \( 4x - 5y = -5 \)

To solve for \( y \), isolate \( y \) on one side of the equation:

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

Subtract \( 4x \) from both sides:

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

Now, divide both sides by \( -5 \):

\[
y = \frac{-4x - 5}{-5}
\]

Simplify:

\[
y = \frac{4}{5}x + 1
\]

So, \( y = \frac{4}{5}x + 1 \).

---

### e. Graph: \( 4x - 5y = -5 \)

This is the equation of a straight line. To graph it, use the intercepts found earlier:
- The \( x \)-intercept is \( x = -\frac{5}{4} \) or \( x = -1.25 \),
- The \( y \)-intercept is \( y = 1 \).

You can plot these two points on the graph:
- \( (-1.25, 0) \)
- \( (0, 1) \)

Then, draw a line through these two points.

---

Would you like any further details or help with another step? Here are some related questions:

1. How do we check if a solution is correct for a linear equation?
2. Can you explain how to calculate intercepts of more complex functions?
3. What is the significance of the slope in the equation \( y = \frac{4}{5}x + 1 \)?
4. How would we solve this equation graphically using a different method?
5. What would happen if the equation had a higher degree (like a quadratic)?

**Tip:** When graphing a line, the slope is crucial. In the equation \( y = \frac{4}{5}x + 1 \), the slope \( \frac{4}{5} \) tells us that for every 5 units we move horizontally (along the \( x \)-axis), we move 4 units vertically (along the \( y \)-axis).

Solve the equation 4x - 5y = -5 for x and y, find intercepts, and graph the line.

Learn how to solve the linear equation 4x - 5y = -5. This tutorial covers key algebraic concepts, including solving for x and y, finding intercepts, and graphing the line. Suitable for students in Grades 8-10.

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