To find the equation of a line given a point and a slope, we use the point-slope form of a linear equation:

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

where:

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

Given:

• Point: $(3, -5)$
• Slope: $m = -\frac{3}{4}$

Solution:

Substitute the given values into the point-slope form:

$y - (-5) = -\frac{3}{4}(x - 3)$

Simplify this:

$y + 5 = -\frac{3}{4}(x - 3)$

Now, distribute $-\frac{3}{4}$:

$y + 5 = -\frac{3}{4}x + \frac{9}{4}$

To get it in slope-intercept form ($y = mx + b$), subtract 5 from both sides:

$y = -\frac{3}{4}x + \frac{9}{4} - 5$

Convert $-5$ to a fraction with a common denominator of 4:

$y = -\frac{3}{4}x + \frac{9}{4} - \frac{20}{4}$

Combine the fractions:

$y = -\frac{3}{4}x - \frac{11}{4}$

Final Answer:

The equation of the line in slope-intercept form is:

$y = -\frac{3}{4}x - \frac{11}{4}$

Would you like a more detailed explanation or have any questions?

Here are 5 related questions you might find helpful:

1. How do you convert point-slope form to slope-intercept form?
2. What is the general form of a linear equation?
3. How do you find the y-intercept given a point and a slope?
4. What is the significance of the slope in a linear equation?
5. How can you graph a line given its equation in slope-intercept form?

Tip: When converting between forms of linear equations, always ensure you simplify fractions and combine like terms for a clean final equation.