Derive the equation of the line in slope-intercept form.
The coordinates are (0, 4), (1, 8)
First, we need to find the slope of the line using the given coordinates.
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
By substituting the coordinates (0, 4) and (1, 8) into the formula, we get:
m = (8 - 4) / (1 - 0)
m = 4 / 1
m = 4
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Taking the point (0, 4) as (x1, y1) and the slope as 4, we get:
y - 4 = 4(x - 0)
y - 4 = 4x
Finally, rearrange the equation into slope-intercept form (y = mx + b) by isolating y:
y = 4x + 4
Therefore, the equation of the line in slope-intercept form is y = 4x + 4.
Write the equation of the line in slope-intercept form.
The coordinates are (0, 2), (1, -1)
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (0, 2) and (1, -1):
m = (-1 - 2) / (1 - 0)
m = -3 / 1
m = -3
Now, we have the slope of the line. Let's use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Taking the point (0, 2) as (x1, y1) and the slope as -3, we get:
y - 2 = -3(x - 0)
y - 2 = -3x
Now, let's rearrange the equation into slope-intercept form (y = mx + b) by isolating y:
y = -3x + 2
Therefore, the equation of the line in slope-intercept form is y = -3x + 2.
Write the equation of the line in slope-intercept form.
The coordinates are (0, -2), (3, 0)
First, we need to find the slope of the line using the given coordinates.
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
By substituting the coordinates (0, -2) and (3, 0) into the formula, we get:
m = (0 -(-2)) / (3 - 0)
m = 2 / 3
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Taking the point (0, -2) as (x1, y1) and the slope as 2/3, we get:
y - (-2) = (2/3)(x - 0)
y + 2 = (2/3)x
Finally, rearrange the equation into slope-intercept form (y = mx + b) by isolating y:
y = (2/3)x - 2
Therefore, the equation of the line in slope-intercept form is y = (2/3)x - 2.
Jonas is saving money for an upcoming vacation. He currently has $50 in his savings account. He plans to add $3 each week. Write an equation that represents the relationship between the amount of money, y, and the number of weeks, x. Use the slope-intercept form y = mx +b.
Given that Jonas currently has $50 in his savings account and he plans to add $3 each week, we can write the equation representing the relationship between the amount of money (y) and the number of weeks (x) as:
y = 3x + 50
In this equation:
- m is the slope, which represents the rate at which Jonas is adding money each week. In this case, the slope is 3.
- b is the y-intercept, which represents the initial amount of money Jonas had in his account. In this case, the y-intercept is 50.
Therefore, the equation in slope-intercept form that represents the relationship between the amount of money (y) and the number of weeks (x) is y = 3x + 50.
On a field trip, one chaperone is required for every 15 students. Is this a proportional or a non-proportional situation?
Enter 1 if this is a proportional situation. Enter 2 if this is a non-proportional situation.
This is a non-proportional situation.
In a proportional situation, the relationship between the two quantities remains constant regardless of the values. In this case, the number of chaperones required is not directly proportional to the number of students since the ratio changes based on the number of students. For every 15 students, one chaperone is required, so the ratio of students to chaperones is not constant.