Using the graph, derive the equation of the line in slope-intercept form, (0,-4),(1,-1)
We can use the slope-intercept form of a linear equation, which is given by:
y = mx + b
where m is the slope and b is the y-intercept.
To find the slope, we can use the formula:
m = (y2 - y1)/(x2 - x1)
Using the points (0,-4) and (1,-1), we can substitute the values into the formula:
m = (-1 - (-4))/(1 - 0)
m = (-1 + 4)/1
m = 3/1
m = 3
Now, we substitute the slope (m) and one of the points (x1, y1) into the equation:
y = mx + b
-4 = 3(0) + b
-4 = 0 + b
b = -4
Now, we have the slope (m = 3) and the y-intercept (b = -4).
Therefore, the equation of the line in slope-intercept form is:
y = 3x - 4
To find the equation of the line in slope-intercept form, we need to determine the slope (m) and the y-intercept (b).
Given two points (0, -4) and (1, -1), we can find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Let's substitute the values of the points into the formula:
m = (-1 - (-4)) / (1 - 0)
m = (-1 + 4) / (1 - 0)
m = 3 / 1
m = 3
Now that we have the slope (m), we can use one of the points and the slope to find the y-intercept (b) using the formula:
y = mx + b
We'll use the point (0, -4):
-4 = 3(0) + b
-4 = 0 + b
b = -4
Now we have the slope (m = 3) and the y-intercept (b = -4).
The equation of the line in slope-intercept form is:
y = 3x - 4