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.

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!