Use the image to answer the question.

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=−2x−1
y equals negative 2 x minus 1

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

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

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

To find the equation of the line that passes through the points A(-2, 0) and B(0, -1), we first need to find the slope (m) using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Taking the coordinates of point A as (x1, y1) = (-2, 0) and point B as (x2, y2) = (0, -1), we plug in the values:

\[ m = \frac{-1 - 0}{0 - (-2)} = \frac{-1}{2} \]

The slope (m) is \(-\frac{1}{2}\). Now, we can use the point-slope form of the equation of a line:

\[ y - y_1 = m(x - x_1) \]

Using point A (-2, 0) for (x1, y1):

\[ y - 0 = -\frac{1}{2}(x - (-2)) \]

This simplifies to:

\[ y = -\frac{1}{2}(x + 2) \]

Distributing:

\[ y = -\frac{1}{2}x - 1 \]

Now, we can also rearrange this to the form:

\[ y = -\frac{1}{2}x - 1 \]

This matches with one of the given options:

y = -\frac{1}{2} x - 1 (Option 3)

Thus, the correct answer is:

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