To find the equation of a line, we can use the point-slope form of the equation:

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

Where:

• $m$ is the slope of the line,
• $(x_1, y_1)$ is a point on the line.

From the information provided:

• The slope $m = \frac{3}{2}$,
• The point on the line is $(5, 7)$.

Substitute these values into the point-slope form:

$y - 7 = \frac{3}{2}(x - 5)$

Now, simplify the equation to get the slope-intercept form $y = mx + b$.

1. Distribute the $\frac{3}{2}$ on the right-hand side:

$y - 7 = \frac{3}{2}x - \frac{15}{2}$

2. Add 7 to both sides to isolate $y$:

$y = \frac{3}{2}x - \frac{15}{2} + 7$

3. Convert 7 into a fraction with denominator 2:

$7 = \frac{14}{2}$

So the equation becomes:

$y = \frac{3}{2}x - \frac{15}{2} + \frac{14}{2}$

4. Combine the constants:

$y = \frac{3}{2}x - \frac{1}{2}$

Thus, the equation of the line is:

$y = \frac{3}{2}x - \frac{1}{2}$

Would you like further details or a more in-depth explanation? Here are some additional questions you might find useful:

1. How would the equation change if the slope was negative?
2. What is the general form of the equation of a line?
3. How can we graph this line based on the equation?
4. How do we find the x-intercept and y-intercept from the equation?
5. How do we convert from point-slope form to slope-intercept form?

Tip: When working with fractions in equations, it's often helpful to convert whole numbers to equivalent fractions to keep things consistent.