graphing equations practice
unit 3 lesson 7
use the image to answer the question
(0,-2), (3,0)
write the equation of the line in slope intercept form
To find the equation of the line in slope-intercept form, we need to find the slope and the y-intercept.
The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
Using the given points (0, -2) and (3, 0), the slope (m) can be calculated as:
m = (0 - (-2)) / (3 - 0)
m = 2 / 3
The y-intercept (b) can be found by substituting the coordinates of any point on the line and the slope into the slope-intercept form equation: y = mx + b. Let's use the point (0, -2):
-2 = (2/3)(0) + b
-2 = b
So, the equation of the line in slope-intercept form is:
y = (2/3)x - 2
To write the equation of the line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b) using the given coordinates (0,-2) and (3,0).
Step 1: Calculate the slope (m)
The formula for slope (m) is given by:
m = (y₂ - y₁) / (x₂ - x₁)
Let's substitute the coordinates into the formula:
m = (0 - (-2)) / (3 - 0)
m = 2 / 3
So, the slope (m) is 2/3.
Step 2: Determine the y-intercept (b)
The y-intercept (b) is where the line intersects the y-axis. In this case, we can directly see that the y-intercept is -2.
So, the y-intercept (b) is -2.
Step 3: Write the equation of the line
Now that we have the slope (m) and the y-intercept (b), we can substitute these values into the slope-intercept form equation (y = mx + b).
y = (2/3)x - 2
Therefore, the equation of the line in slope-intercept form is y = (2/3)x - 2.
Note: It is important to note that without the image provided or additional context, I cannot verify if this is the correct equation for the specific problem given in unit 3 lesson 7.
To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b).
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Given the points (0,-2) and (3,0), we can substitute the coordinates into the formula:
m = (0 - (-2)) / (3 - 0)
Simplifying,
m = 2 / 3
Now, we can substitute the slope into the equation y = mx + b, and use one of the given points to solve for the y-intercept.
Using the point (0, -2):
-2 = (2/3) * 0 + b
Simplifying,
-2 = b
Therefore, the equation of the line in slope-intercept form is:
y = (2/3)x - 2