Determine the equation of the line that passes through the points an
. Enter your equation in the form , Simplify your answer
completely.

Ask by Medina Ellis. in the United States

Jan 22,2025

Question

Determine the equation of the line that passes through the points $$ (2,-14) $$ an $$ (8,-68) $$. Enter your equation in the form $$ y=m x+b $$, Simplify your answer completely.

UpStudy AI · Accepted Answer

To determine the equation of the line passing through the points $$ (2, -14) $$ and $$ (8, -68) $$ in the form $$ y = mx + b $$, follow these steps:

1. **Calculate the slope ($$ m $$)**:

The slope $$ m $$ of a line passing through two points $$ (x_1, y_1) $$ and $$ (x_2, y_2) $$ is given by:
   $$
   m = \frac{y_2 - y_1}{x_2 - x_1}
   $$
   
   Plugging in the given points:
   $$
   m = \frac{-68 - (-14)}{8 - 2} = \frac{-68 + 14}{6} = \frac{-54}{6} = -9
   $$

2. **Determine the y-intercept ($$ b $$)**:

Using the slope-intercept form $$ y = mx + b $$ and one of the points, say $$ (2, -14) $$:
   $$
   -14 = (-9)(2) + b
   $$
   $$
   -14 = -18 + b
   $$
   $$
   b = -14 + 18 = 4
   $$

3. **Write the equation of the line**:

Substitute $$ m = -9 $$ and $$ b = 4 $$ into the slope-intercept form:
   $$
   y = -9x + 4
   $$

**Final Answer:**
$$
y = -9x + 4
$$
The equation of the line is $$ y = -9x + 4 $$.

Determine the equation of the line that passes through the points an
. Enter your equation in the form , Simplify your answer
completely.

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Determine the equation of the line that passes through the points an . Enter your equation in the form , Simplify your answer completely.