Write the equation of the linear function that passes through the points (

Question

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:

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