unit 3 lesson 7
graphing equations quick check
use the image to answer the question
using the graph, derive the equation of the line in slope-intercept form.
(0,-4), (1,-1)
y=3x-4
y=3x+4
y=-3x-4
3x-y=4
To find the equation of the line in slope-intercept form, we need to find the slope and the y-intercept.
We can find the slope using the two given points (0, -4) and (1, -1).
The slope is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (0, -4) and (1, -1), we can substitute the values into the formula:
m = (-1 - (-4)) / (1 - 0)
m = 3 / 1
m = 3
Now that we have the slope, we can use the point-slope form of a line to find the equation:
y - y1 = m(x - x1)
Using the point (0, -4), we can substitute the values into the equation:
y - (-4) = 3(x - 0)
y + 4 = 3x
To write the equation in slope-intercept form, we need to isolate y:
y = 3x - 4
So, the equation of the line in slope-intercept form is y = 3x - 4.
To derive the equation of the line in slope-intercept form using the given points (0,-4) and (1,-1), we can calculate the slope and the y-intercept.
Step 1: Calculate the slope (m):
The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (0, -4) and (1, -1):
m = (-1 - (-4)) / (1 - 0)
m = (-1 + 4) / 1
m = 3 / 1
m = 3
Step 2: Calculate the y-intercept (b):
We can use one of the given points and the slope to calculate the y-intercept (b) using the slope-intercept form (y = mx + b).
Using the point (1, -1) and the slope m = 3:
-1 = 3(1) + b
-1 = 3 + b
Now, solve for b:
b = -1 - 3
b = -4
Step 3: Write the equation in slope-intercept form:
Using the values of m and b, the equation of the line in slope-intercept form is:
y = 3x - 4
Therefore, the correct answer is:
y = 3x - 4.
To derive the equation of the line in slope-intercept form using the given graph, you will need to find the slope and the y-intercept.
First, let's find the slope:
The slope of a line can be found using the formula:
slope = (change in y) / (change in x)
Using the coordinate points (0, -4) and (1, -1):
(change in y) = (-1) - (-4) = 3
(change in x) = 1 - 0 = 1
Therefore, the slope = 3 / 1 = 3.
Next, let's find the y-intercept:
The y-intercept is the point where the line crosses the y-axis. From the graph, we can see that the y-intercept is -4.
Now that we have the slope (3) and the y-intercept (-4), we can write the equation in slope-intercept form, which is: y = mx + b
where:
m = slope
b = y-intercept
Thus, the equation of the line in slope-intercept form is y = 3x - 4.