Question

find the equation of the line that cuts through (0, 5) and (1, 2)?
a. $y = -3x + 5$ \t\t\tc. $y = -5x + 3$
b. $y = 3x + 5$ \t\t\t\td. $y = -dfrac{1}{3}x + 5$

please select the best answer from the choices provided

○ a
○ b
○ c
○ d

Explanation:

Step1: Find the slope (m)

The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Using points \((0, 5)\) (where \(x_1 = 0, y_1 = 5\)) and \((1, 2)\) (where \(x_2 = 1, y_2 = 2\)):
\( m = \frac{2 - 5}{1 - 0} = \frac{-3}{1} = -3 \).

Step2: Use slope-intercept form (\(y = mx + b\))

The y-intercept (\(b\)) is the y-value when \(x = 0\). From the point \((0, 5)\), \(b = 5\).
Substitute \(m = -3\) and \(b = 5\) into \(y = mx + b\):
\( y = -3x + 5 \), which matches option a.

Answer:

A. \( y = -3x + 5 \)