Write the equation of the line that passes through the given points. $$ \left(\frac{1}{8}, \frac{1}{2}\right) \text { and }\left(\frac{3}{8}, 0\right) $$ The equation of the line is $$ \square $$ (Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)

Question

UpStudy AI · Accepted Answer

1. Calculate the slope $$ m $$ using the formula  
   $$
   m = \frac{y_2 - y_1}{x_2 - x_1}
   $$
   where $$ (x_1, y_1) = \left(\frac{1}{8}, \frac{1}{2}\right) $$ and $$ (x_2, y_2) = \left(\frac{3}{8}, 0\right) $$.

2. Substitute the points into the slope formula:  
   $$
   m = \frac{0 - \frac{1}{2}}{\frac{3}{8} - \frac{1}{8}} = \frac{-\frac{1}{2}}{\frac{2}{8}} = \frac{-\frac{1}{2}}{\frac{1}{4}}.
   $$

3. Simplify the slope:  
   $$
   m = -\frac{1}{2} \times \frac{4}{1} = -2.
   $$

4. Use the point-slope form of the equation:  
   $$
   y - y_1 = m(x - x_1)
   $$
   Substituting $$ m = -2 $$ and $$ (x_1, y_1) = \left(\frac{1}{8}, \frac{1}{2}\right) $$, we get:  
   $$
   y - \frac{1}{2} = -2\left(x - \frac{1}{8}\right).
   $$

5. Distribute the slope:  
   $$
   y - \frac{1}{2} = -2x + \frac{2}{8}.
   $$
   Since $$ \frac{2}{8} = \frac{1}{4} $$, this becomes:  
   $$
   y - \frac{1}{2} = -2x + \frac{1}{4}.
   $$

6. Solve for $$ y $$ by adding $$ \frac{1}{2} $$ to both sides:  
   $$
   y = -2x + \frac{1}{4} + \frac{1}{2}.
   $$

7. Combine the constant terms by writing $$ \frac{1}{2} $$ as $$ \frac{2}{4} $$:  
   $$
   y = -2x + \frac{1}{4} + \frac{2}{4} = -2x + \frac{3}{4}.
   $$

The equation of the line is $$ y = -2x + \frac{3}{4} $$.
The equation of the line is $$ y = -2x + \frac{3}{4} $$.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Algebra Questions