The given equation is in point-slope form:

$y - y_1 = m(x - x_1)$

In this case, the equation provided is:

$y - 5 = \frac{9}{7}(x + 4)$

Explanation of the terms:

• $m = \frac{9}{7}$ is the slope of the line.
• $(x_1, y_1) = (-4, 5)$ is the point through which the line passes.

Steps to Graph the Line:

1. Identify the point: The line passes through the point $(-4, 5)$. This is the point of intersection on the graph where the line crosses.

2. Slope: The slope $\frac{9}{7}$ means for every 7 units you move to the right (positive direction of x), the line moves up by 9 units (positive direction of y).

3. Start graphing: From the point $(-4, 5)$, you can use the slope to plot another point by moving 7 units to the right and 9 units up. This gives you a second point, allowing you to draw the line.

Would you like further details or examples on graphing or slopes?

Follow-up questions:

1. How would you rewrite the equation into slope-intercept form?
2. How can you determine if two lines are parallel?
3. What is the effect of changing the slope in the equation of a line?
4. Can you explain the relationship between point-slope and slope-intercept forms of a line?
5. How do you find the equation of a line that is perpendicular to the given line?

Tip:

Remember that in slope-intercept form, the equation of a line is written as $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.