Question

write a slope-intercept equation for a line that passes through \\((-3,1)\\) and \\((2,-14)\\).

the slope-intercept equation for the line is \\(\square\\).
(simplify your answer. type an integer or a simplified fraction. type an equation.)

Explanation:

Identify the given points

We are given two points on the line:

$$ (x_1, y_1) = (-3, 1) \quad \text{and} \quad (x_2, y_2) = (2, -14) $$

Calculate the slope

Using the Slope from Two Points knowledge point:

$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-14 - 1}{2 - (-3)} = \frac{-15}{5} = -3 $$

Use point-slope form

Using the Point-Slope Form knowledge point with the point \((-3, 1)\) and slope \(m = -3\):

$$ y - y_1 = m(x - x_1) $$

$$ y - 1 = -3(x - (-3)) $$

$$ y - 1 = -3(x + 3) $$

Convert to slope-intercept form

Using the Slope-Intercept Form knowledge point, we solve for \(y\):

$$ y - 1 = -3x - 9 $$

$$ y = -3x - 8 $$

Answer:

Write a slope-intercept equation for a line that passes through \( (-3,1) \) and \( (2,-14) \).

The slope-intercept equation for the line is <blank>\(y = -3x - 8\)</blank>.
(Simplify your answer. Type an integer or a simplified fraction. Type an equation.)