Use the image to answer the question.
A coordinate plane of 4 quadrants shows x and y axes ranging from negative 3 to 3 in increments of 1. A line with arrows at each end intercepts two plotted points, A and B. Point A is plotted at left parenthesis negative 2 comma 0 right parenthesis. Point B is plotted at left parenthesis 0 comma negative 1 right parenthesis. The coordinates are not labeled.
Which of the following is the equation of the line on the graph?
(1 point)
Responses
A) y=−1/2x−1
y equals negative Start Fraction 1 over 2 End Fraction x minus 1
B) y=−1/2x−2
y equals negative Start Fraction 1 over 2 End Fraction x minus 2
C) y=1/2x−1
y equals Start Fraction 1 over 2 End Fraction x minus 1
D) y=−2x−1
The equation of the line passing through points A and B can be found by calculating the slope using the coordinates of the two points.
The slope of the line passing through points A (-2,0) and B (0,-1) can be calculated as:
m = (change in y) / (change in x)
m = (-1 - 0) / (0 - (-2))
m = -1 / 2
m = -1/2
Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation:
y - y1 = m(x - x1)
(x1,y1) = (-2,0)
y - 0 = -1/2(x - (-2))
y = -1/2(x + 2)
y = -1/2x - 1
Therefore, the correct answer is:
A) y = -1/2x - 1