Question 8 of 10 Which is not an equation of the line going through (6,7) and (2,-1) 7 A. y=2x-5 B. y+1=2(x-2) C y-1=2(x+2) D y-7=2(x-6)

To determine which equation is not the equation of the line going through the points $(6,7)$ and $(2,-1)$, we need to find the slope of the line and then use the point-slope form of a linear equation to find the equation of the line.<br /><br />Step 1: Find the slope of the line.<br />The slope of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:<br />\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]<br /><br />Substituting the given points $(6,7)$ and $(2,-1)$ into the formula, we get:<br />\[ m = \frac{-1 - 7}{2 - 6} = \frac{-8}{-4} = 2 \]<br /><br />Step 2: Use the point-slope form of a linear equation.<br />The point-slope form of a linear equation is given by:<br />\[ y - y_1 = m(x - x_1) \]<br /><br />Using the point $(6,7)$ and the slope $m=2$, we can write the equation as:<br />\[ y - 7 = 2(x - 6) \]<br /><br />Step 3: Simplify the equation.<br />To simplify the equation, we can distribute the 2 on the right side:<br />\[ y - 7 = 2x - 12 \]<br /><br />Adding 7 to both sides, we get:<br />\[ y = 2x - 5 \]<br /><br />Therefore, the equation of the line going through the points $(6,7)$ and $(2,-1)$ is $y = 2x - 5$.<br /><br />Step 4: Compare the given options with the equation we found.<br />A. $y=2x-5$ - This matches our equation, so it is correct.<br />B. $y+1=2(x-2)$ - Let's simplify this equation:<br /> \[ y + 1 = 2x - 4 \]<br /> Subtracting 1 from both sides:<br /> \[ y = 2x - 5 \]<br /> This also matches our equation, so it is correct.<br />C. $y-1=2(x+2)$ - Let's simplify this equation:<br /> \[ y - 1 = 2x + 4 \]<br /> Adding 1 to both sides:<br /> \[ y = 2x + 5 \]<br /> This does not match our equation, so it is incorrect.<br />D. $y-7=2(x-6)$ - This matches our equation, so it is correct.<br /><br />Therefore, the equation that is not the equation of the line going through the points $(6,7)$ and $(2,-1)$ is option C: $y-1=2(x+2)$.