Derive the equation of the line in slope-intercept form.
(1 point)
(0,4) and (1,8)
The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope of the line passing through (0,4) and (1,8), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the values from the given points:
m = (8 - 4) / (1 - 0)
m = 4 / 1
m = 4
So, the slope of the line is 4.
Now, we can substitute the value of m into the slope-intercept form equation:
y = 4x + b
To find the value of b, we can choose either of the given points. Let's use (0,4):
4 = 4(0) + b
4 = 0 + b
b = 4
So, 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 two pieces of information: the slope of the line (m) and the y-intercept (b).
The formula for calculating the slope (m) is:
m = (y₂ - y₁) / (x₂ - x₁)
Let's use the given coordinates to calculate the slope:
m = (8 - 4) / (1 - 0)
m = 4 / 1
m = 4
Now that we have the slope (m), we can use one of the given points (0,4) to calculate the y-intercept (b) using the formula:
b = y - mx
Let's substitute the values into the formula:
b = 4 - 4(0)
b = 4 - 0
b = 4
Now we can write the equation of the line in slope-intercept form:
y = mx + b
Substituting the values of m and b, we have:
y = 4x + 4
Therefore, the equation of the line in slope-intercept form is y = 4x + 4.