Using the graph, derive the equation of the line in slope-intercept form, (0, 4),(1, 8)
First, we need to find the slope of the line using the two points (0,4) and (1,8):
Slope (m) = (y2 - y1) / (x2 - x1)
m = (8 - 4) / (1 - 0)
m = 4
Now, we will use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept. We can use one of the given points to find the value of b:
Using point (0, 4):
4 = 4(0) + b
4 = b
Now we can write the equation of the line:
y = 4x + 4
Therefore, the equation of the line in slope-intercept form is y = 4x + 4.
Using the graph, derive the equation of the line in slope-intercept form, (0, 2),(1, -1)
First, we need to find the slope of the line using the two points (0,2) and (1,-1):
Slope (m) = (y2 - y1) / (x2 - x1)
m = (-1 - 2) / (1 - 0)
m = -3 / 1
m = -3
Now, we will use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept. We can use one of the given points to find the value of b:
Using point (0, 2):
2 = -3(0) + b
2 = b
Now we can write the equation of the line:
y = -3x + 2
Therefore, the equation of the line in slope-intercept form is y = -3x + 2.
Using the graph, derive the equation of the line in slope-intercept form, (3, 0) , (0, -2)
To find the equation of a line in slope-intercept form, we first need to calculate the slope of the line using the coordinates (3, 0) and (0, -2).
Slope (m) = (y2 - y1) / (x2 - x1)
m = (-2 - 0) / (0 - 3)
m = -2 / -3
m = 2/3
Now that we have the slope (m = 2/3), we can use one of the points to find the y-intercept (b) in the slope-intercept form of a linear equation (y = mx + b). Let's use point (3, 0):
0 = (2/3)*3 + b
0 = 2 + b
b = -2
Now we have the slope (m = 2/3) and the y-intercept (b = -2), so we can write the equation of the line in slope-intercept form:
y = (2/3)x - 2
Therefore, the equation of the line in slope-intercept form is y = (2/3)x - 2.