Question
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
y=−12x−2
y equals negative Start Fraction 1 over 2 End Fraction x minus 2
y=12x−1
y equals Start Fraction 1 over 2 End Fraction x minus 1
y=−2x−1
y equals negative 2 x minus 1
y=−12x−1
The correct equation of the line on the graph is: y = -1/2x - 1
This can be determined by finding the slope of the line passing through the points A(-2,0) and B(0,-1).
Slope (m) = (y2 - y1) / (x2 - x1)
m = (-1 - 0) / (0 - (-2))
m = (-1) / (2)
m = -1/2
Therefore, the equation of the line in slope-intercept form (y = mx + b) would be:
y = -1/2x + b
Using either point A or B to solve for b:
0 = (-1/2)(-2) + b
0 = 1 + b
b = -1
Therefore, the equation of the line is: y = -1/2x - 1
Therefore, the correct response is: y equals negative Start Fraction 1 over 2 End Fraction x minus 1.