We need to find f(0) for the function f(x) = x + 7. To evaluate f(0), we substitute x = 0 into the function. f(0) = 0 + 7 = 7. The answer is 7, which corresponds to choice A. This represents the y-intercept of the linear function where the graph crosses the y-axis. Choice B incorrectly identifies the coefficient of x as the y-intercept.

The correct answer is A (1, 2). The midpoint formula averages the x-coordinates and the y-coordinates separately: x = (4 + (−2)) ÷ 2 = 2 ÷ 2 = 1; y = (−3 + 7) ÷ 2 = 4 ÷ 2 = 2. Midpoint = (1, 2). B (2, 4) uses the sums without dividing by 2: (4 + (−2)) = 2 and (−3 + 7) = 4. C (3, 5) drops the negative signs: (4 + 2) ÷ 2 = 3 and (3 + 7) ÷ 2 = 5. D (6, −10) likely comes from subtracting or doubling instead of averaging. Always divide both sums by 2 — the midpoint is literally the average of the two endpoints.

We need to find the y-intercept of the line y = -2x + 9. In the slope-intercept form y = mx + b, the y-intercept is the value of b, which is the constant term. From y = -2x + 9, we can see that b = 9. The y-intercept is 9, meaning when x = 0 (at day 0), the plant's height is 9 inches. Choice A (-2) incorrectly identifies the slope as the y-intercept.

We need to identify which equation has slope -4 and y-intercept 6. In slope-intercept form y = mx + b, we need m = -4 and b = 6. This gives us y = -4x + 6, which matches choice A exactly. The negative slope indicates the line falls steeply from left to right, and the positive y-intercept means it crosses the y-axis above the origin. Choice B has the wrong signs for both slope and y-intercept, while choices C and D switch the roles of slope and y-intercept.

We need to find f(0) for the function f(x) = -5x + 9. To evaluate f(0), we substitute x = 0 into the function. f(0) = -5(0) + 9 = 0 + 9 = 9. The answer is 9, which corresponds to choice A. This represents the y-intercept of the linear function where the graph crosses the y-axis. Choice B incorrectly uses the coefficient of x instead of the constant term.

This question asks for f(0) in the linear function f(x) = -4x + 20, which models the initial gift card balance before purchases. f(0) is the y-intercept, found by substituting x = 0 into the equation: f(0) = -4(0) + 20 = 20. This value represents the starting balance, with the slope -4 indicating the cost per snack. The structure y = mx + b directly shows b as the intercept. The correct answer is 20, which is choice D. A key distractor is choice A, -4, confusing the slope with the intercept. Another is choice C, 16, possibly from miscalculating -4(1) + 20 or another small error.

We need to find the y-intercept of the line $y = 3x + 5$. In slope-intercept form $y = mx + b$, the y-intercept is the constant term b. Looking at $y = 3x + 5$, we can see that b = 5. The y-intercept is the value of y when x = 0, which gives us $y = 3(0) + 5 = 5$. Choice B correctly identifies the y-intercept as 5. Choice A confuses the slope (3) with the y-intercept.

This question asks for the slope of the line passing through the points (1,2) and (5,14), which represents the constant rate of change in the drone's height over time. To find the slope, use the formula m = (y₂ - y₁)/(x₂ - x₁), substituting the given points. Here, m = (14 - 2)/(5 - 1) = 12/4 = 3, emphasizing how the change in y over the change in x gives the rate. This calculation shows the slope is positive 3, meaning the height increases by 3 meters per second. The correct answer is 3, which is choice B. A key distractor is choice A, which is 1/3, likely from reversing the numerator and denominator in the slope formula. Another common error is choice C, -3, which might result from confusing the order of subtraction and adding a negative sign incorrectly.

We need to identify the equation with slope 5 and y-intercept -1. Using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we get y = 5x + (-1), which simplifies to y = 5x - 1. Looking at the choices, option A correctly shows y = 5x - 1. Choice D incorrectly has y-intercept +1 instead of -1, while choice B has the wrong slope sign (negative instead of positive).

We need to write the equation for a bike rental cost with a $6 fixed fee plus $3 per hour. In the form y = mx + b, the slope m represents the rate per hour ($3) and the y-intercept b represents the fixed fee ($6). Therefore, the equation is y = 3x + 6. Choice B (y = 3x - 6) has the correct slope but makes the y-intercept negative, while choice D reverses the sign of the slope.