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−1
y equals negative Start Fraction 1 over 2 End Fraction x minus 1

y=−2x−1
y equals negative 2 x minus 1

y=12x−1
y equals Start Fraction 1 over 2 End Fraction x minus 1

y=−12x−2
y equals negative Start Fraction 1 over 2 End Fraction x minus 2
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Answer 1

The equation of the line can be found by using the two points that are plotted, A(-2,0) and B(0,-1).

First, calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1)
m = (-1 - 0) / (0 - (-2))
m = -1 / 2
m = -1/2

Next, use the slope-intercept form of the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.

Now, plug in the slope (-1/2) and one of the points to find b:
0 = (-1/2)(-2) + b
0 = 1 + b
b = -1

Therefore, the equation of the line is:
y = -1/2x -1

The answer is:
y equals negative 1/2 x minus 1