Derive the equation of the line in slope intercept form (0,4), (1,8)
To derive the equation of the line in slope-intercept form, we need to find the slope of the line (m) and the y-intercept (b).
Slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Given points:
(x1, y1) = (0, 4)
(x2, y2) = (1, 8)
Applying the slope formula:
m = (8 - 4) / (1 - 0)
m = 4 / 1
m = 4
Therefore, the slope of the line is 4.
Now, let's substitute one of the points (1, 8) into the slope-intercept form equation: y = mx + b.
8 = 4(1) + b
Simplifying:
8 = 4 + b
To find the value of b, we subtract 4 from both sides of the equation:
8 - 4 = b
4 = b
Therefore, the y-intercept (b) is 4.
The equation of the line in slope-intercept form is:
y = 4x + 4.
To derive the equation of a line in slope-intercept form (y = mx + b), you need to find the slope (m) and the y-intercept (b) using the given points.
Step 1: Find the slope (m)
The formula for slope (m) is given by:
m = (y2 - y1) / (x2 - x1)
Using the given points (0,4) and (1,8), we can substitute the values into the slope 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)
We can use the slope-intercept form of a line (y = mx + b) and substitute one of the given points' coordinates (0,4) to solve for b:
4 = 4(0) + b
4 = b
So, the y-intercept (b) is 4.
Step 3: Write the equation
Now that we have the slope (m = 4) and the y-intercept (b = 4), we can write the equation of the line in slope-intercept form:
y = 4x + 4
Therefore, the equation of the line in slope-intercept form is y = 4x + 4.