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 $x$.