(1,8) (0,4)
Derive the equation of the line in slope-intercept form. (1 point)
To find the equation of the line passing through the points (1,8) and (0,4) in slope-intercept form (y=mx+b), we first need to find the slope (m) of the line.
The slope (m) can be calculated using the formula:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) = (0, 4) and (x2, y2) = (1, 8)
m = (8 - 4)/(1 - 0)
m = 4/1
m = 4
Now that we have the slope (m=4), we can use one of the points (1,8) to find the y-intercept (b).
Using the point-slope formula:
y - y1 = m(x - x1)
y - 8 = 4(x - 1)
y - 8 = 4x - 4
y = 4x + 4
Therefore, the equation of the line passing through the points (1,8) and (0,4) in slope-intercept form is:
y = 4x + 4
To find the equation of the line passing through the points (0,2) and (1,-1) in slope-intercept form (y=mx+b), we first need to find the slope (m) of the line.
The slope (m) can be calculated using the formula:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) = (0, 2) and (x2, y2) = (1, -1)
m = (-1 - 2)/(1 - 0)
m = -3/1
m = -3
Now that we have the slope (m=-3), we can use one of the points (0,2) to find the y-intercept (b).
Using the point-slope formula:
y - y1 = m(x - x1)
y - 2 = -3(x - 0)
y - 2 = -3x
y = -3x + 2
Therefore, the equation of the line passing through the points (0,2) and (1,-1) in slope-intercept form is:
y = -3x + 2
To find the equation of the line passing through the points (3,0) and (0,-2) in slope-intercept form (y=mx+b), we first need to find the slope (m) of the line.
The slope (m) can be calculated using the formula:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) = (3, 0) and (x2, y2) = (0, -2)
m = (-2 - 0)/(0 - 3)
m = -2/-3
m = 2/3
Now that we have the slope (m=2/3), we can use one of the points (3,0) to find the y-intercept (b).
Using the point-slope formula:
y - y1 = m(x - x1)
y - 0 = (2/3)(x - 3)
y = (2/3)x - 2
Therefore, the equation of the line passing through the points (3,0) and (0,-2) in slope-intercept form is:
y = (2/3)x - 2
Since Jonas currently has $50 in his savings account and plans to add $3 each week, we can represent the relationship between the amount of money (y) and the number of weeks (x) using the equation in slope-intercept form.
The initial amount in his account is $50, which corresponds to the y-intercept. Each week he adds $3, which represents the slope of the line.
Therefore, the equation that represents the relationship is:
y = 3x + 50
In this equation:
- y represents the total amount of money in Jonas's savings account.
- x represents the number of weeks that have passed.
- The slope of the line (m) is 3, indicating that $3 is added to his savings each week.
- The y-intercept (b) is 50, representing the initial amount of money in his savings account.
(0,2) (1,-1)
Write the equation of the line in slope-intercept form. (1 point)
(3,0) (0,-2)
Write the equation of the line in slope-intercept form. (1 point)
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 .(1 point)
On a field trip, one chaperone is required for every 15 students. Is this a proportional or a nonproportional situation? Enter 1 if this is a proportional situation. Enter 2 if this is a nonproportional situation. (1 point)
This is a nonproportional situation.
In a proportional relationship, the ratio of the quantities remains constant. However, in this situation, the number of chaperones required is not directly proportional to the number of students. The requirement of one chaperone for every 15 students is a fixed rule and does not change based on the number of students. Therefore, it is a nonproportional situation.
Please enter 2 to indicate that this is a nonproportional situation.