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)
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To find the equation of the line in slope-intercept form, we need to determine the slope and the y-intercept.
To find the slope, we can use the two given points (0, 2) and (1, -1).
Slope (m) = (change in y)/(change in x)
m = (-1 - 2)/(1 - 0)
m = -3/1
m = -3
Now, we can use the slope-intercept form of a line: y = mx + b, where m is the slope and b is the y-intercept.
We already know the slope is -3, so the equation becomes:
y = -3x + b
To find the y-intercept (b), we can substitute one of the given points into the equation.
Using the point (0, 2):
2 = -3(0) + b
2 = 0 + b
2 = b
So, the y-intercept is 2.
Now we can write the equation in slope-intercept form:
y = -3x + 2
To write the equation of the line in slope-intercept form, we need to find the slope and the y-intercept.
First, let's find the slope. The slope is the change in y divided by the change in x. We can calculate it using the given points (0, 2) and (1, -1).
Slope = (y2 - y1) / (x2 - x1)
= (-1 - 2) / (1 - 0)
= -3 / 1
= -3
Now, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
Since we have the slope (-3), we just need to find the y-intercept. Looking at the graph, we can see that the line intersects the y-axis at y = 2. Therefore, the y-intercept (b) is 2.
Finally, we can write the equation of the line in slope-intercept form:
y = -3x + 2