Question

question 7
identify which equation does not correspond to the following coordinates: (11, 22) and (-12, -15).
○ 37x - 23y = 99
○ y + 15 = \frac{37}{23}(x + 12)
○ y - 22 = \frac{37}{23}(x - 11)
○ y = \frac{37}{23}x + \frac{99}{23}

Explanation:

Step1: Find the slope between the two points

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 points \((11, 22)\) and \((- 12,-15)\), we have \( x_1 = 11,y_1 = 22,x_2=-12,y_2=-15 \). So \( m=\frac{-15 - 22}{-12 - 11}=\frac{-37}{-23}=\frac{37}{23} \).

Step2: Check the point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \).

• For the point \((11,22)\), the equation is \( y - 22=\frac{37}{23}(x - 11) \) (matches the third option).
• For the point \((-12,-15)\), the equation is \( y+15=\frac{37}{23}(x + 12) \) (matches the second option).

Step3: Convert point - slope to slope - intercept form

Starting from \( y - 22=\frac{37}{23}(x - 11) \), expand it:
\( y-22=\frac{37}{23}x-\frac{37\times11}{23} \)
\( y=\frac{37}{23}x-\frac{407}{23}+22 \)
\( y=\frac{37}{23}x-\frac{407}{23}+\frac{506}{23} \)
\( y=\frac{37}{23}x+\frac{99}{23} \) (matches the fourth option).

Step4: Convert slope - intercept to standard form

Starting from \( y=\frac{37}{23}x+\frac{99}{23} \), multiply both sides by 23:
\( 23y = 37x+99 \)
\( 37x-23y=- 99 \) (not \( 37x - 23y = 99 \) as in the first option)

Answer:

\( 37x - 23y = 99 \) (the first option)