Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line.
Containing the points and
The equation is
(Type an equation. Simplify your answer.)

Question

Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line.
Containing the points

and

The equation is
(Type an equation. Simplify your answer.)

UpStudy AI · Accepted Answer

To find the equation of the line passing through the points $$ (3, 6) $$ and $$ (5, 5) $$, follow these steps:

1. **Calculate the slope (m):**
   
   $$
   m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 6}{5 - 3} = \frac{-1}{2} = -\frac{1}{2}
   $$

2. **Use the slope-intercept form (y = mx + b) and plug in one of the points to find $$ b $$:**
   
   Using the point $$ (3, 6) $$:
   
   $$
   6 = -\frac{1}{2}(3) + b \
   6 = -\frac{3}{2} + b \
   b = 6 + \frac{3}{2} = \frac{12}{2} + \frac{3}{2} = \frac{15}{2}
   $$

3. **Write the final equation:**
   
   $$
   y = -\frac{1}{2}x + \frac{15}{2}
   $$

**Final Answer:**

$$
y = -\frac{1}{2}x + \frac{15}{2}
$$
The equation of the line is $$ y = -\frac{1}{2}x + \frac{15}{2} $$.

Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line.
Containing the points and
The equation is
(Type an equation. Simplify your answer.)

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Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line. Containing the points and The equation is (Type an equation. Simplify your answer.)

Solución de inteligencia artificial de Upstudy

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Solución

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Latest Algebra Questions

Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line.
Containing the points and
The equation is
(Type an equation. Simplify your answer.)