Interpret the equation y=−4x+10. What type of function does this equation define? Describe its graph.(1 point)
Responses
This is a linear function. Its graph is a straight line with a slope of −4 and a y-intercept of 10.
This is a linear function. Its graph is a straight line with a slope of , negative 4, and a , y, -intercept of 10.
This is a nonlinear function. Its graph is a curve.
This is a nonlinear function. Its graph is a curve.
This is a linear function. Its graph is a straight line with a y-intercept of −4 and a slope of 10.
This is a linear function. Its graph is a straight line with a , y, -intercept of , negative 4, and a slope of 10.
This is a nonlinear function. Its graph has a maximum at (0,10).
This is a linear function. Its graph is a straight line with a slope of −4 and a y-intercept of 10.
The equation of a function is y=2x−6. If this function were graphed, what would its y-intercept be?(1 point)
Responses
−3
−6
6
2
The y-intercept of the function y=2x−6 is -6.
Use the table to answer the question.
x y
4 38
6 58
Write the equation of the linear function that models the relationship shown in the table.
(1 point)
Responses
y=10x−2
y equals 10 x minus 2
y=−10x+78
y equals negative 10 x plus 78
y=10x+2
y equals 10 x plus 2
y=x+34
y equals x plus 34
Using the given values of x and y, we can find the slope of the line as:
slope (m) = (change in y) / (change in x) = (58-38) / (6-4) = 20/2 = 10
Now, we can use the slope and any of the given points to find the y-intercept (b) using the slope-intercept form:
y = mx + b
Substituting the values of m, x, and y from the table:
38 = 10(4) + b
b = 38 - 40 = -2
Therefore, the equation of the linear function that models the relationship shown in the table is y = 10x - 2.
Oliwia is opening a bank account. She learns that there is a special promotion where if she deposits $3,000 and then makes no additional deposits or withdrawals, her account will earn $3 in interest per month. Write the equation of a linear function that models the relationship between number of months and total amount of money Oliwia will have in her account.(1 point)
Responses
y=1,000x+3, where x is the number of months and y is the total amount of money Oliwia will have in her account.
, y equals 1,000 x plus 3, , where , x, is the number of months and , y, is the total amount of money Oliwia will have in her account.
y=3x+1,000, where x is the number of months and y is the total amount of money Oliwia will have in her account.
, y equals 3 x plus 1,000, , where , x, is the number of months and , y, is the total amount of money Oliwia will have in her account.
y=3x+3,000, where x is the number of months and y is the total amount of money Oliwia will have in her account.
y equals 3 x plus 3,000, , where , x, is the number of months and , y, is the total amount of money Oliwia will have in her account.
y=3,000x+3, where x is the number of months and y is the total amount of money Oliwia will have in her account.
The initial deposit of $3,000 remains constant and earns $3 in interest per month. Therefore, the total amount of money (y) in Oliwia's account after x months can be represented by the equation:
y = 3x + 3000
Therefore, the correct answer is y=3x+3,000, where x is the number of months and y is the total amount of money Oliwia will have in her account.