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The equation given is \( y = 4x - 5 \), which is a linear equation in slope-intercept form, \( y = mx + b \), where:

- \( m = 4 \) is the slope.
- \( b = -5 \) is the y-intercept, the point where the line crosses the y-axis.

### Plotting the Line:
1. **Y-Intercept**: The line crosses the y-axis at \( y = -5 \) (point \( (0, -5) \)).
2. **Slope**: The slope \( 4 \) means that for every increase of 1 unit in \( x \), \( y \) increases by 4 units. This can be seen as a "rise over run" of \( \frac{4}{1} \), i.e., for every 1 unit move right along the x-axis, the line goes up 4 units.

### Points to Plot:
- Start with the y-intercept at \( (0, -5) \).
- From this point, move 1 unit to the right (increase \( x \) by 1) and then 4 units up (increase \( y \) by 4). This gives the next point: \( (1, -1) \).
- Similarly, you can move 1 more unit right to \( x = 2 \) and 4 units up to \( y = 3 \), giving the point \( (2, 3) \).

By plotting these points, you can draw the line representing the equation on the graph.

Do you have any questions, or would you like a detailed explanation on any part of this?

Here are some related questions you could explore:
1. What happens to the graph if the slope is negative?
2. How would the line shift if the y-intercept changed to \( -3 \)?
3. How can you find the x-intercept of this line?
4. What is the general effect of increasing the slope on the steepness of the line?
5. How would the graph look if the equation were \( y = -4x + 5 \)?

**Tip**: To find the x-intercept, set \( y = 0 \) and solve for \( x \).

Graph the linear equation y = 4x - 5 on the provided grid.

Learn how to graph the linear equation y = 4x - 5 by identifying the slope and y-intercept. This problem covers key algebraic concepts including graphing linear equations, interpreting slope, and plotting points. Suitable for students in Grades 7-9.

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