Question
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.
To find the equation of a line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b).
First, let's calculate the slope using the two given points: (0, 2) and (1, -1).
The slope (m) can be found using the formula: m = (y2 - y1)/(x2 - x1)
m = (-1 - 2)/(1 - 0)
m = -3/1
m = -3
Now that we have the slope, we can use one of the given points and the slope to find the y-intercept (b).
Let's use the point (0, 2), so we can substitute the values into the slope-intercept form:
2 = -3(0) + b
2 = 0 + b
2 = b
Therefore, the equation of the line is y = -3x + 2 in slope-intercept form.
To write the equation of the line in slope-intercept form, we need to find the slope (m) and the y-intercept (b).
Given two points on the line, (0, 2) and (1, -1), we can use the formula for slope (m):
m = (y2 - y1) / (x2 - x1)
Using the coordinates (0, 2) for (x1, y1) and (1, -1) for (x2, y2), we can calculate the slope:
m = (-1 - 2) / (1 - 0)
m = -3 / 1
m = -3
Now that we have the slope, we can plug it into the slope-intercept form, which is written as:
y = mx + b
Using the coordinate (0, 2), we can substitute the values for x and y, and the slope:
2 = -3(0) + b
2 = b
So, the y-intercept (b) of the line is 2.
Therefore, the equation of the line in slope-intercept form is:
y = -3x + 2