Question

 which equation represents the line that passes through the points (3, 7) and (-1, -1)?

Answer 1

points: (3, 7) and (-1, -1)

slope (m) :

$\sf \dfrac{y_2-y_1}{x_2-x_1}$

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$\hookrightarrow \dfrac{-1-7}{-1-3}$

$\hookrightarrow \dfrac{-8}{-4}$

$\hookrightarrow 2$

Equation:

$\sf y-y_1 = m(x-x_1)$

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$\rightarrow \sf y-7 = 2(x-3)$

$\rightarrow \sf y = 2x-6+7$

$\rightarrow \sf y = 2x+1$

Answer 2

Answer:

$y = 2x- 1$

Step-by-step explanation:

To determine which equation passes through the points (3, 7) and (-1, -1), we need to determine the slope of the equation. Then, we shall use point slope form to determine the equation of the line.

Determining the slope of the line:

$\text{Slope} = \dfrac{\text{Rise}}{\text{Run} } =\dfrac{\text{y}_{2} - \text{y}_{1} }{\text{x}_{2} - \text{x}_{1} }$

Substituting the points in the slope formula:

$\text{Slope} =\dfrac{-1 - 7 }{-1- 3 }$

Simplifying the slope:

$\text{Slope} =\dfrac{-1 - 7 }{-1- 3 }$

$\text{Slope} =\dfrac{-8}{-4 } = 2$

Determining the equation of the line:

We shall use point slope form to determine the equation of the line.

$\text{Point slope form:} \ y - y_{1} = m(x- x_{1} )$

Substitute the slope and the coordinates of any two points stated above.

$y -7= 2(x- 3 ) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Using the point (3,7)}]$

Simplify the equation and organize it to slope intercept form:

$y -7= 2x- 6$

$y = 2x- 6 + 7$

$y = 2x+ 1$