https://file.aiquickdraw.com/mathbot/file/17296397410508aaxfd8j.jpg

You have uploaded an image that includes the equation \( y = 4x - 5 \) and a coordinate plane. Let's analyze and graph the line corresponding to this equation step by step.

### Step 1: Identify the equation form
The given equation \( y = 4x - 5 \) is in slope-intercept form, which is:

\[
y = mx + b
\]

Where:
- \( m \) is the slope (rate of change).
- \( b \) is the y-intercept (the point where the line crosses the y-axis).

From the equation:
- **Slope \( m = 4 \)**: This means that for every 1 unit increase in \( x \), \( y \) increases by 4.
- **Y-intercept \( b = -5 \)**: The line crosses the y-axis at the point \( (0, -5) \).

### Step 2: Plot the y-intercept
The y-intercept is \( (0, -5) \). On the graph, locate the point where the line crosses the y-axis, which is at \( y = -5 \).

### Step 3: Use the slope to find another point
The slope is 4, meaning that for every 1 unit increase in \( x \), \( y \) increases by 4. Starting from \( (0, -5) \):
- Move 1 unit to the right on the x-axis (from \( x = 0 \) to \( x = 1 \)).
- Then move 4 units up on the y-axis (from \( y = -5 \) to \( y = -1 \)).

So another point on the line is \( (1, -1) \).

### Step 4: Draw the line
Connect the points \( (0, -5) \) and \( (1, -1) \) with a straight line. Extend the line in both directions to complete the graph of the equation \( y = 4x - 5 \).

### Step 5: Positive Slope Confirmation
The word "positive" written near the equation is a reminder that the line has a positive slope, meaning it increases as \( x \) increases, which is correct for this graph.

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Would you like more details or have any questions about this graph or the equation? Here are 5 related questions for further exploration:

1. What would the graph look like if the slope was negative instead of positive?
2. How would the graph change if the y-intercept was 0 instead of -5?
3. Can you determine the x-intercept of this line, where \( y = 0 \)?
4. How can you find the equation of a line parallel to \( y = 4x - 5 \)?
5. How would you graph the line if the equation was in point-slope form instead of slope-intercept form?

**Tip**: The slope tells you how steep the line is—higher absolute values of slope indicate a steeper line!

Graph the equation y = 4x - 5 and analyze its key features.

Understand how to graph the linear equation y = 4x - 5 using the slope-intercept form. This guide will walk you through identifying the slope, plotting the y-intercept, and drawing the line step by step. Perfect for students in Grades 8-10.

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