Question

1. a relationship between x and y is shown on the graph.

complete the equation that best describes the relationship between x and y.
choose the correct answer from each drop - down menu to complete the equation
(y=) select (x+) select

1. a student made a model of the washington monument using a scale in which 1 inch represents 15 feet. the actual height of the washington monument is approximately 555 feet. which measurement is closest to the height of the model in inches?

a. 37 in.
b. 75 in.
c. 46 in.
d. 180 in.

Explanation:

Question 3

Step1: Identify slope (m)

The line passes through points, e.g., \((0, 4)\) (y-intercept) and \((-2, 0)\). Slope \(m = \frac{4 - 0}{0 - (-2)} = \frac{4}{2} = 2\).

Step2: Identify y-intercept (b)

When \(x = 0\), \(y = 4\), so \(b = 4\)? Wait, no, looking at the graph again—wait, the y-intercept: when \(x=0\), the line crosses y-axis at \(y = 4\)? Wait, no, let's check another point. Wait, maybe I misread. Wait, the line goes through \((-2, 0)\) and \((0, 4)\)? Wait, no, let's recalculate. Wait, from \(x=-2\) to \(x=0\), \(x\) increases by 2, \(y\) increases by 4 (from 0 to 4), so slope \(m = \frac{4}{2} = 2\). Y-intercept is when \(x=0\), \(y=4\)? Wait, but the equation is \(y = mx + b\). Wait, maybe the graph has y-intercept at \(y = 4\)? Wait, no, let's check the grid. Wait, the y-axis: when \(x=0\), the line is at \(y = 4\)? Wait, maybe I made a mistake. Wait, another approach: the slope-intercept form is \(y = mx + b\), where \(m\) is slope and \(b\) is y-intercept. Let's take two points: \((-2, 0)\) and \((0, 4)\). So slope \(m = \frac{4 - 0}{0 - (-2)} = 2\). Y-intercept \(b = 4\)? Wait, but the options for the first dropdown (coefficient of x) are -2, 2, -4, 4. The second dropdown (constant term) is -2, 2, -4, 4. Wait, maybe I misread the graph. Wait, maybe the line passes through \((0, 4)\) and \((-2, 0)\), so slope is 2, y-intercept is 4? Wait, but let's check another point: when \(x = -1\), \(y = 2\)? Wait, no, if \(y = 2x + 4\), then when \(x=-1\), \(y = 2(-1) + 4 = 2\), which matches. So the equation is \(y = 2x + 4\)? Wait, but the first dropdown is for the coefficient of x (m), second for b. So first dropdown: 2, second dropdown: 4? Wait, but the options for the second dropdown are -2, 2, -4, 4. So yes, \(m = 2\), \(b = 4\)? Wait, maybe I made a mistake. Wait, let's check the graph again. Wait, the line goes through \((-2, 0)\) and \((0, 4)\), so slope is 2, y-intercept 4. So the equation is \(y = 2x + 4\).

Step1 (correction): Wait, maybe the y-intercept is 4? Wait, the first dropdown (x coefficient) is 2, second (constant) is 4. So the equation is \(y = 2x + 4\).

Step1: Set up proportion

Scale: 1 inch = 15 feet. Let \(x\) be the model height (inches). Actual height = 555 feet. So \(\frac{1}{15} = \frac{x}{555}\).

Step2: Solve for x

Cross-multiply: \(15x = 555\) → \(x = \frac{555}{15} = 37\).

Answer:

\(y = \boldsymbol{2}x + \boldsymbol{4}\) (So first dropdown: 2, second dropdown: 4)

Question 4