unit 3 lesson 7
graphing equations practice
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 (y = mx + b), we need to first find the slope of the line using the given points (0,4) and (1,8).
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points. Plugging in the values, we have:
m = (8 - 4) / (1 - 0)
m = 4 / 1
m = 4
Now that we have the slope, we can calculate the y-intercept (b) using one of the given points. Let's use the point (0,4).
Using the slope-intercept form, we have:
4 = 4(0) + b
This simplifies to:
4 = b
Therefore, the y-intercept (b) is 4.
Finally, we can write the equation of the line in slope-intercept form:
y = 4x + 4
To derive the equation of a line in slope-intercept form, we need to find the slope and the y-intercept.
The formula for the slope of a line is:
slope (m) = (change in y) / (change in x)
Using the given points (0,4) and (1,8), we can calculate the slope as follows:
change in y = 8 - 4 = 4
change in x = 1 - 0 = 1
slope (m) = 4 / 1 = 4
Now that we have the slope, we can use the slope-intercept form of a line, which is y = mx + b.
Here, m is the slope and b is the y-intercept, so we need to find the value of b.
We can choose any of the given points to substitute into the equation. Let's use (0,4):
y = mx + b
4 = 4(0) + b
4 = 0 + b
b = 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 determine the slope (m) and the y-intercept (b) of the line.
To find the slope (m), you can use the formula:
m = (change in y)/(change in x)
Given the coordinates (0,4) and (1,8), we can calculate the change in y and change in x as follows:
change in y = 8 - 4 = 4
change in x = 1 - 0 = 1
Now, substitute the values into the slope formula:
m = 4/1 = 4
Once you have determined the slope (m), you can use one of the given points and the slope in the point-slope form of a linear equation:
y - y1 = m(x - x1)
Using the point (0,4) and the slope (m = 4), we can substitute into the equation:
y - 4 = 4(x - 0)
Now, simplify the equation:
y - 4 = 4x
To rewrite the equation in slope-intercept form (y = mx + b), isolate y:
y = 4x + 4
Therefore, the equation of the line in slope-intercept form is y = 4x + 4.