Question

Writing Linear Equations in Slope-Intercept Form Quick Check
4 of 54 of 5 Items








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 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

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

y=−2x−1

Answer 1

To determine the equation of the line that passes through the points A (-2, 0) and B (0, -1), we can follow these steps:

1. **Calculate the Slope (m)**: The slope formula is given by:

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

Using the points A (-2, 0) and B (0, -1):
- \( (x_1, y_1) = (-2, 0) \)
- \( (x_2, y_2) = (0, -1) \)

Plugging in these values:

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

2. **Use Point-Slope Form**: The point-slope form of the equation of a line is:

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

Using point B (0, -1) and the slope we calculated:

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

Simplifying this gives:

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

Subtracting 1 from both sides:

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

3. **Equation in Slope-Intercept Form**: The equation is now in slope-intercept form \(y = mx + b\) where \(m = -\frac{1}{2}\) and \(b = -1\).

Thus, the equation of the line represented by the graph is:

**y = -\frac{1}{2}x - 1**

So, the correct response is:

**y = -\frac{1}{2}x - 1**.