graphing equations unit 3 lesson 7
use the image to answer the question
(0,2) (1,-1)
write the equation of the line in slope-intercept form.
To find the equation of the line in slope-intercept form, we need to determine the slope and y-intercept.
First, let's find the slope (m). We can use the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (0,2) and (1,-1):
m = (-1 - 2) / (1 - 0)
m = -3 / 1
m = -3
Next, let's find the y-intercept (b). The y-intercept is the value of y when x = 0. From the given coordinates, we can see that the y-intercept is 2.
Now, we can write the equation in slope-intercept form:
y = mx + b
y = -3x + 2
So, the equation of the line in slope-intercept form is y = -3x + 2.
To write the equation of a line in slope-intercept form (y = mx + b), you need to determine the values of the slope (m) and the y-intercept (b).
To find the slope (m), you can use the formula:
m = (y2 - y1) / (x2 - x1)
Given the points (0,2) and (1,-1), you can substitute the respective coordinates into the formula:
m = (-1 - 2) / (1 - 0)
m = -3
The slope of the line is -3.
To find the y-intercept (b), you can select one of the given points and substitute its coordinates into the equation (y = mx + b). Let's use the point (0,2):
2 = (-3)(0) + b
2 = b
The y-intercept (b) is 2.
Now that we have the slope and the y-intercept, we can write the equation of the line in slope-intercept form:
y = -3x + 2
Therefore, the equation of the line is y = -3x + 2.
To find the equation of the line in slope-intercept form, we need to determine the slope of the line (m) and the y-intercept (b).
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (0,2) and (1,-1), we can substitute the values into the formula:
m = (-1 - 2) / (1 - 0)
m = -3 / 1
m = -3
Now, we have the slope (m) of -3.
To find the y-intercept (b), we can substitute one of the given points into the slope-intercept form equation (y = mx + b) and then solve for b.
Using the point (0,2), we substitute the values into the equation:
2 = -3(0) + b
2 = 0 + b
b = 2
So, the y-intercept (b) is 2.
Now, we can write the equation of the line in slope-intercept form:
y = mx + b
Substituting the values we found, we get:
y = -3x + 2
Therefore, the equation of the line in slope-intercept form is y = -3x + 2.