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
To find the equation of the line passing through points A and B, we first need to find the slope of the line.
The slope formula is given by:
m = (y2 - y1) / (x2 - x1)
Let's designate point A as (x1, y1) = (-2, 0) and point B as (x2, y2) = (0, -1)
Plugging in the values:
m = (-1 - 0) / (0 - (-2))
m = -1 / 2
m = -1/2
Next, we use the point-slope form of the equation of a line, where a point P(x1, y1) on the line and the slope m is given by:
(y - y1) = m(x - x1)
Using point B (0, -1) and the slope -1/2, we have:
(y - (-1)) = (-1/2)(x - 0)
y + 1 = (-1/2)x
y = (-1/2)x - 1
Therefore, the equation of the line passing through points A and B is:
y = (-1/2)x - 1
So, the correct answer is:
y equals negative Start Fraction 1 over 2 End Fraction x minus 1