(1,-1)(0,-4) Using the graph, derive the equation of the line in slope-intercept form.
To derive the equation of the line in slope-intercept form, we need to find the slope and y-intercept of the line.
The slope (m) of a line can be found using the formula:
m = (change in y) / (change in x)
Given the two points (1, -1) and (0, -4), we can calculate the change in y and change in x:
Change in y = -1 - (-4) = -1 + 4 = 3
Change in x = 1 - 0 = 1
Plugging these values into the formula, we get:
m = 3/1 = 3
Using the slope-intercept form of a line (y = mx + b), we can substitute the slope (m) and one of the given points (1, -1) to find the y-intercept (b).
Plugging in the values, we get:
-1 = 3(1) + b
-1 = 3 + b
b = -1 - 3
b = -4
Therefore, the equation of the line in slope-intercept form is:
y = 3x - 4
To derive the equation of a line in slope-intercept form, we need to find the slope and y-intercept.
Step 1: Find the slope.
The slope of a line can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Given the two points (1, -1) and (0, -4), we can substitute the coordinates into the formula:
m = (-4 - (-1)) / (0 - 1) = (-4 + 1) / (0 - 1) = -3 / -1 = 3
So, the slope of the line is 3.
Step 2: Find the y-intercept.
The y-intercept is the value of y when x = 0. We can use either of the two given points to find the y-intercept.
Using the point (0, -4):
y = mx + b (where m is the slope and b is the y-intercept)
-4 = 3(0) + b
-4 = b
So, the y-intercept is -4.
Step 3: Write the equation in slope-intercept form.
Now that we have the slope (m = 3) and the y-intercept (b = -4), we can write the equation of the line in slope-intercept form, which is y = mx + b.
Therefore, the equation of the line is:
y = 3x - 4
To derive the equation of the line in slope-intercept form, we need to find the slope and the y-intercept.
1. Finding the slope:
The slope (m) of a line can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Given the points (1, -1) and (0, -4), we can substitute the coordinates into the formula:
m = (-4 - (-1)) / (0 - 1)
m = (-4 + 1) / (0 - 1)
m = -3 / -1
m = 3
2. Finding the y-intercept:
The y-intercept (b) is the value where the line crosses the y-axis. We can find it by substituting the coordinates of one of the points (x, y) and the slope (m) into the slope-intercept form and solving for b.
Let's take the point (1, -1):
y = mx + b
-1 = 3(1) + b
-1 = 3 + b
b = -1 - 3
b = -4
Now we have the slope (m = 3) and the y-intercept (b = -4), so we can write the equation of the line in slope-intercept form:
y = 3x - 4
Therefore, the equation of the line in slope-intercept form is y = 3x - 4.