Question

Choose the point-slope form of the equation below that represents the line that passes through the points (-6,4) and (2,0)Options: A.) y - 4 = -1/2 (x + 6) B.) y - 4 = 2(x + 6)C.) y + 6 = -1/2 (x - 4) D.) y + 6 = 2(x - 4)

Answer 1

y - 4 = -1/2 (x +6) (option A)

Step-by-step explanation:

we apply the slope-form formula:

`y-y_1=m(x-x_1)`

The points: (-6,4) and (2,0) = (x1, y1) and (x2, y2)

`\begin{gathered} \text{slope formula = }m\text{ = }(y_2-y_1)/(x_2-x_1) \\ m\text{ = }(0-4)/(2-(-6))=(-4)/(2+6)=(-4)/(8) \\ m\text{ = -1/2} \end{gathered}`

we pick any of the points and insert into the point-slope formula:

Using point (-6, 4)

y - 4 = -1/2 (x -(-6))

y - 4 = -1/2 (x +6)

Hence, the point-slope form of the equation below that represents the line that passes through the points (-6,4) and (2,0) is y - 4 = -1/2 (x +6) (option A)