Question

question 1
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 standard form?
\\( x - 33y = -702 \\)
\\( 33x - y = -702 \\)
\\( 33x + y = -702 \\)
\\( x + 33y = -702 \\)

Explanation:

Step1: Find the slope

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

Step2: Use point - slope form

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:
\( y-(-22)=-\frac{1}{33}(x - 24) \)
\( y + 22=-\frac{1}{33}x+\frac{24}{33} \)

Step3: Convert to standard form

Multiply through by 33 to clear the fraction:
\( 33(y + 22)=-x + 24 \)
\( 33y+726=-x + 24 \)
Add \( x \) to both sides and subtract 726 from both sides:
\( x+33y=24 - 726 \)
\( x + 33y=-702 \)

Answer:

\( x + 33y=-702 \) (the last option: \( x + 33y=-702 \))