Question

write a slope-intercept equation for a line that passes through \\((-3, 7.5)\\) and \\((0, 7.5)\\).

the slope-intercept equation for the line is \\(\square\\).
(use integers or decimals for any numbers in the equation.)

Explanation:

Identify the given points

We are given two points on the line:
\(P_1(x_1, y_1) = (-3, 7.5)\)
\(P_2(x_2, y_2) = (0, 7.5)\)

Calculate the slope

Using the Slope from Two Points knowledge point:

$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$

$$ m = \frac{7.5 - 7.5}{0 - (-3)} = \frac{0}{3} = 0 $$

Determine the y-intercept

Using the Slope-Intercept Form knowledge point:
The y-intercept is the point where \(x = 0\).
The given point \((0, 7.5)\) directly gives:

$$ b = 7.5 $$

Write the equation

Using the Horizontal Lines knowledge point:
Since the slope \(m = 0\), the line is horizontal.
Substituting \(m = 0\) and \(b = 7.5\) into \(y = mx + b\):

$$ y = 0x + 7.5 $$

$$ y = 7.5 $$

Answer:

Write a slope-intercept equation for a line that passes through \((-3, 7.5)\) and \((0, 7.5)\).

The slope-intercept equation for the line is <blank>\(y = 7.5\)</blank>.
(Use integers or decimals for any numbers in the equation.)