Question: Write the equation of the line that passes through the given points.
(2,2.5) and (0, - 2.5)
The equation of the line is □.
(Simplify your answer. Type your answer in slope-intercept form. Use integers or decimals for any numbers in the equation.)
1. **State the problem:** Find the equation of the line passing through the points $ (2, 2.5) $ and $ (0, -2.5) $.
2. **Formula used:** The slope-intercept form of a line is $$ y = mx + b $$ where $ m $ is the slope and $ b $ is the y-intercept.
3. **Calculate the slope $ m $:**
$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2.5 - 2.5}{0 - 2} = \frac{-5}{-2} = 2.5 $$
4. **Find the y-intercept $ b $:** Use one point, for example $ (0, -2.5) $:
$$ y = mx + b \Rightarrow -2.5 = 2.5 \times 0 + b \Rightarrow b = -2.5 $$
5. **Write the equation:**
$$ y = 2.5x - 2.5 $$
6. **Final answer:** The equation of the line in slope-intercept form is
$$ y = 2.5x - 2.5 $$