Writing Linear Equations in Slope-Intercept Form Quick Check

Question

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.