Question: User: 1314 Review for Quiz 1
Question 12 of 15 (7 points) | Question Attempt: 1 of 1
(a) Use slope-intercept form to write an equation of the line that passes through the two given points.
(b) Write the equation using function notation where y = f(x).
(-2, 5) and (-1, 10)
Part 1 of 2
The equation of the line in slope-intercept form is .
Part 2 of 2
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1. **State the problem:** Find the equation of the line passing through the points $(-2, 5)$ and $(-1, 10)$ in slope-intercept form and then write it in function notation.
2. **Find the slope $m$ using the formula:**
$$m = \frac{y_2 - y_1}{x_2 - x_1}$$
where $(x_1, y_1) = (-2, 5)$ and $(x_2, y_2) = (-1, 10)$.
3. **Calculate the slope:**
$$m = \frac{10 - 5}{-1 - (-2)} = \frac{5}{-1 + 2} = \frac{5}{1} = 5$$
4. **Use the slope-intercept form equation:**
$$y = mx + b$$
where $m = 5$ and $b$ is the y-intercept.
5. **Substitute one point to find $b$:** Using point $(-2, 5)$,
$$5 = 5(-2) + b$$
$$5 = -10 + b$$
$$b = 5 + 10 = 15$$
6. **Write the equation in slope-intercept form:**
$$y = 5x + 15$$
7. **Write the equation in function notation:**
$$f(x) = 5x + 15$$
**Final answers:**
- Slope-intercept form: $y = 5x + 15$
- Function notation: $f(x) = 5x + 15$