Question

A line has a slope of
–
3
4
and passes through the point (16,
–
18). Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer 1

To write the equation of a line in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we can follow these steps:

1. **Identify the slope and a point on the line**:
The slope \( m = -\frac{3}{4} \) and we have the point \( (16, -18) \).

2. **Use the point-slope form of the line equation**:
The point-slope form is given by \( y - y_1 = m(x - x_1) \). Here, \( (x_1, y_1) = (16, -18) \):
\[
y - (-18) = -\frac{3}{4}(x - 16)
\]
This simplifies to:
\[
y + 18 = -\frac{3}{4}(x - 16)
\]

3. **Distribute the slope on the right-hand side**:
\[
y + 18 = -\frac{3}{4}x + \frac{3}{4} \times 16
\]
Calculate \( \frac{3}{4} \times 16 = 12 \):
\[
y + 18 = -\frac{3}{4}x + 12
\]

4. **Isolate \( y \)** by subtracting 18 from both sides:
\[
y = -\frac{3}{4}x + 12 - 18
\]
Simplify \( 12 - 18 = -6 \):
\[
y = -\frac{3}{4}x - 6
\]

5. **Final equation**:
The equation of the line in slope-intercept form is:
\[
y = -\frac{3}{4}x - 6
\]

This is the required equation of the line.