graphing equations unit 3 lesson 7
use the image to answer the question
(0,4), (1,8)
derive 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 the y-intercept.
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1),
where (x1, y1) = (0, 4) and (x2, y2) = (1, 8).
m = (8 - 4) / (1 - 0)
m = 4 / 1
m = 4
Now that we have the slope, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1),
where (x1, y1) = (0, 4).
Plugging in the values:
y - 4 = 4(x - 0)
Simplifying:
y - 4 = 4x
Finally, rearranging the equation to slope-intercept form (y = mx + b):
y = 4x + 4
Therefore, the equation of the line in slope-intercept form is y = 4x + 4.
To derive the equation of a line in slope-intercept form, we need the slope and the y-intercept.
Step 1: Find the slope (m) using the given points (0,4) and (1,8).
The formula to find the slope is:
m = (y2 - y1) / (x2 - x1)
Let's substitute the coordinates:
m = (8 - 4) / (1 - 0)
m = 4 / 1
m = 4
So, the slope (m) is 4.
Step 2: Use one of the given points and the slope in the slope-intercept form equation (y = mx + b) to determine the y-intercept (b).
Let's use the point (0,4):
4 = 4(0) + b
4 = 0 + b
b = 4
So, the y-intercept (b) is 4.
Step 3: Now we can write the equation of the line using the slope (m = 4) and the y-intercept (b = 4).
The equation of the line in slope-intercept form is:
y = mx + b
Substituting the values, we get:
y = 4x + 4
Therefore, the equation of the line in slope-intercept form is y = 4x + 4.
To derive the equation of the line in slope-intercept form, you need to find the slope of the line and the y-intercept.
Step 1: Find the slope (m):
The slope (m) is calculated using the formula:
m = (y2 - y1) / (x2 - x1)
In this case, we have two points:
Point 1: (x1, y1) = (0, 4)
Point 2: (x2, y2) = (1, 8)
Substituting the values into the formula:
m = (8 - 4) / (1 - 0)
m = 4 / 1
m = 4
So, the slope (m) of the line is 4.
Step 2: Find the y-intercept (b):
The y-intercept (b) is the value of y when x is 0.
From the given coordinates, we know that the line passes through the point (0, 4).
Therefore, the y-intercept (b) is 4.
Step 3: Write the equation in slope-intercept form (y = mx + b):
Now that we have the values of the slope (m) and the y-intercept (b), we can substitute them into the slope-intercept form equation:
y = mx + b
Substituting the values:
y = 4x + 4
So, the equation of the line in slope-intercept form is y = 4x + 4.