Question

question 2
2 points
given the coordinates of (24, -22) and (-9, -21), what would be the equation of the line that corresponds to the coordinates in slope-intercept form?
\\( y = -\frac{1}{33}x - \frac{234}{11} \\)
\\( y = \frac{1}{33}x - \frac{234}{11} \\)
\\( y = -33x - 702 \\)
\\( y = 33x + 702 \\)

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Let \((x_1, y_1)=(24, - 22)\) and \((x_2, y_2)=(-9, - 21)\).
Then \( m=\frac{-21-(-22)}{-9 - 24}=\frac{-21 + 22}{-33}=\frac{1}{-33}=-\frac{1}{33} \).

Step2: Use point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Let's use the point \((24,-22)\).
Substitute \( m =-\frac{1}{33} \), \( x_1 = 24 \) and \( y_1=-22 \) into the point - slope form:
\( y-(-22)=-\frac{1}{33}(x - 24) \)
\( y + 22=-\frac{1}{33}x+\frac{24}{33} \)
Simplify \(\frac{24}{33}=\frac{8}{11}\)
\( y=-\frac{1}{33}x+\frac{8}{11}-22 \)
Convert \( 22\) to elevenths: \( 22=\frac{242}{11} \)
\( y=-\frac{1}{33}x+\frac{8 - 242}{11} \)
\( y=-\frac{1}{33}x-\frac{234}{11} \)

Answer:

\( y =-\frac{1}{33}x-\frac{234}{11} \) (corresponding to the first option: \( y =-\frac{1}{33}x-\frac{234}{11} \))