Question

Write the equation of the linear function that passes through the points (
4
4,
−
3
−3) and (
−
6
−6,
8
8).

Answer 1

To find the equation of the linear function that passes through the points \((4, -3)\) and \((-6, 8)\), we can follow these steps:

1. **Calculate the slope (m)** of the line using the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let \((x_1, y_1) = (4, -3)\) and \((x_2, y_2) = (-6, 8)\).

\[
m = \frac{8 - (-3)}{-6 - 4} = \frac{8 + 3}{-6 - 4} = \frac{11}{-10} = -\frac{11}{10}
\]

2. **Use the point-slope form of the equation** of a line:

\[
y - y_1 = m(x - x_1)
\]

Using the point \((4, -3)\) and the slope \(-\frac{11}{10}\):

\[
y - (-3) = -\frac{11}{10}(x - 4)
\]

This simplifies to:

\[
y + 3 = -\frac{11}{10}(x - 4)
\]

3. **Distribute and rearrange to slope-intercept form (y = mx + b)**:

\[
y + 3 = -\frac{11}{10}x + \frac{11 \cdot 4}{10}
\]
\[
y + 3 = -\frac{11}{10}x + \frac{44}{10}
\]
\[
y + 3 = -\frac{11}{10}x + \frac{22}{5}
\]

Now, subtract 3 (or \( \frac{15}{5} \)) from both sides:

\[
y = -\frac{11}{10}x + \frac{22}{5} - \frac{15}{5}
\]
\[
y = -\frac{11}{10}x + \frac{7}{5}
\]

4. **Final equation**:

Thus, the equation of the linear function is:

\[
y = -\frac{11}{10}x + \frac{7}{5}
\]