(1,8)(0,4) 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 (m) and the y-intercept (b).
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (1,8) and (0,4):
m = (8 - 4) / (1 - 0)
m = 4 / 1
m = 4
Now, let's find the y-intercept (b). We can use the point (0,4) and the slope (m) in the slope-intercept form equation:
y = mx + b
Using the point (0,4):
4 = 4(0) + b
4 = 0 + b
b = 4
Therefore, the slope-intercept form equation of the line is:
y = 4x + 4
To derive the equation of a line in slope-intercept form, you need two pieces of information: the slope of the line and a point on the line. From the given points (1,8) and (0,4), we can find the slope using the formula:
slope (m) = (y2 - y1) / (x2 - x1)
Let's calculate the slope:
m = (8 - 4) / (1 - 0)
m = 4 / 1
m = 4
Now that we have the slope (m = 4), we can use one of the given points to find the y-intercept (b), which is where the line intersects the y-axis. Let's use the point (1,8):
y = mx + b
8 = 4(1) + b
8 = 4 + b
b = 8 - 4
b = 4
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 = 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 (y = mx + b), we need to find the slope (m) and the y-intercept (b) using the given points (1,8) and (0,4).
Step 1: Find the slope (m):
The slope can be calculated using the formula: m = (y2 - y1) / (x2 - x1)
Let's assign the first point as (x1, y1) = (1,8) and the second point as (x2,y2) = (0,4).
m = (4 - 8) / (0 - 1)
m = -4 / -1
m = 4
Step 2: Find the y-intercept (b):
Now that we have the slope, we can use one of the given points to find the y-intercept (b) using the formula: y = mx + b.
Using the point (1,8):
8 = 4(1) + b
8 = 4 + b
b = 8 - 4
b = 4
Step 3: Write the equation in slope-intercept form:
We have the slope (m = 4) and the y-intercept (b = 4), so we can write the equation in slope-intercept form: y = mx + b.
Therefore, the equation of the line is y = 4x + 4 in slope-intercept form.