To graph the line with a slope of 3 passing through the point $(-2, 5)$, follow these steps:

1. Identify the Slope-Intercept Form of a Line:

The equation of a line can be written as: $y = mx + b$ where $m$ is the slope, and $b$ is the y-intercept.

2. Use the Given Information:

We know:

• The slope $m = 3$
• The line passes through the point $(-2, 5)$, which we will use to solve for the y-intercept $b$.

3. Find the y-Intercept:

Substitute the point $(-2, 5)$ into the slope-intercept form: $5 = 3(-2) + b$ $5 = -6 + b$ $b = 5 + 6 = 11$ So, the equation of the line is: $y = 3x + 11$

4. Plot the Line:

• Plot the point $(-2, 5)$ on the graph.
• Since the slope is 3, which means "rise over run" is $3/1$, move 3 units up and 1 unit to the right from the point $(-2, 5)$ to find another point on the line.
• Continue this pattern or use the equation $y = 3x + 11$ to plot other points like $(0, 11)$ or $(1, 14)$.

Would you like further details on this, or have any questions?

Here are some related questions for further practice:

1. How do you find the slope of a line from two given points?
2. What is the general form of a linear equation?
3. How can you convert a linear equation from slope-intercept form to standard form?
4. How would the line change if the slope were negative?
5. How do you graph vertical and horizontal lines?

Tip: Remember, slope $m$ is the ratio of how much the line rises vertically compared to how much it moves horizontally.