Question

Which equation is a point slope form equation for line AB?

Responses

y+5=−2(x−2)
y plus 5 equals negative 2 left parenthesis x minus 2 right parenthesis

y+6=−2(x−1)
y plus 6 equals negative 2 left parenthesis x minus 1 right parenthesis

y+2=−2(x−5)
y plus 2 equals negative 2 left parenthesis x minus 5 right parenthesis

y+1=−2(x−6)
y minus 1 equals negative 2 left parenthesis x minus 6 right parenthesis
A graph with a line running through point A, with coordinates (1, 6), and point B, with coordinates (5, -2)

Answer 1

The correct point-slope form equation for line AB is y + 6 = -2(x - 1), which is obtained by calculating the slope between points A and B and then using one of the points to express the equation.

Step-by-step explanation:

The question asks to identify the point-slope form equation for line AB that passes through points A (1, 6) and B (5, -2). To find this, we calculate the slope (m) of the line using the two points:

1. Calculate the slope using the formula: m = (y2 - y1) / (x2 - x1). For points A (1, 6) and B (5, -2), m = (-2 - 6) / (5 - 1) = -8 / 4 = -2.
2. Use the slope and one of the points to write the point-slope form: y - y1 = m(x - x1). Using point A, it would be y - 6 = -2(x - 1).

Comparing the given options with our calculated point-slope form, we can see that the correct equation is y + 6 = -2(x - 1).

Answer 2

Option 3

Step-by-step explanation:

The slope is
`(-2-6)/(5-1)=-2`.

The equation of the line through
`(x_1, y_1)` with slope
`m` is
`y-y_1=m(x-x_1)`.