Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 2 right parenthesis and left parenthesis 1 comma negative 1 right parenthesis.
Write the equation of the line in slope-intercept form.
(1 point)
To write the equation of the line in slope-intercept form, we need to find the slope and the y-intercept.
To find the slope, we can use the two given points (0,2) and (1,-1). The slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (0,2) and (1,-1):
m = (-1 - 2) / (1 - 0)
m = -3 / 1
m = -3
Now that we have the slope, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Using the point (0,2):
y - 2 = -3(x - 0)
y - 2 = -3x
Now, rearranging the equation to slope-intercept form (y = mx + b):
y = -3x + 2
So, the equation of the line in slope-intercept form is y = -3x + 2.
wrong
I apologize for the incorrect response. I will try again.
To find the equation of the line, we can use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
To find the slope (m), we use the formula:
m = (change in y) / (change in x)
Using the points (0,2) and (1,-1), we can calculate the slope:
m = (-1 - 2) / (1 - 0)
m = -3 / 1
m = -3
Now, we have the slope (-3).
To find the y-intercept (b), we can substitute the coordinates of one of the points into the equation:
2 = -3(0) + b
2 = 0 + b
b = 2
Therefore, the y-intercept is 2.
Now we can write the equation of the line in slope-intercept form:
y = mx + b
Substituting the values of m and b:
y = -3x + 2
So, the equation of the line in slope-intercept form is y = -3x + 2.
To find the equation of the line in slope-intercept form, we need to determine the slope and y-intercept of the line.
First, let's find the slope using the two given points.
Slope (m) = (y2 - y1) / (x2 - x1)
Using the points (0, 2) and (1, -1):
m = (-1 - 2) / (1 - 0)
m = -3 / 1
m = -3
Now, we have the slope of the line. To find the y-intercept (b), we can use the point-slope form of a line equation:
y - y1 = m(x - x1)
Using the point (0, 2):
y - 2 = -3(x - 0)
y - 2 = -3x
To convert this to slope-intercept form (y = mx + b), we can isolate y:
y = -3x + 2
Hence, the equation of the line in slope-intercept form is y = -3x + 2.