Question

1. the graph of a linear function is shown on the coordinate plane. which equation is best represented by this graph? a. $y = 3x + 12$ b. $y = 1.5x + 12$ c. $y = -3x + 12$ d. $y = -1.5x + 12$

Explanation:

Step1: Determine the slope sign

The graph is decreasing from left to right, so the slope \( m \) is negative. This eliminates options a (\( y = 3x + 12 \)) and b (\( y = 1.5x + 12 \)) since their slopes are positive.

Step2: Find two points on the line

From the graph, we can see that the line passes through \( (0, 12) \) (the y - intercept) and \( (4, 0) \) (the x - intercept).

Step3: Calculate the slope

The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using the points \( (x_1,y_1)=(0,12) \) and \( (x_2,y_2)=(4,0) \), we have \( m=\frac{0 - 12}{4 - 0}=\frac{- 12}{4}=- 3 \)? Wait, no, wait. Wait, let's check the grid again. Wait, maybe the points are \( (0,12) \) and \( (8,0) \)? Wait, no, looking at the graph, when \( x = 0 \), \( y = 12 \), and when \( y = 0 \), let's count the grid. Each grid square is 1 unit? Wait, the x - axis: from \( x = 0 \) to \( x = 4 \), how much does y change? Wait, maybe I made a mistake. Wait, let's take another pair of points. Let's take \( (0,12) \) and \( (2,9) \). Then the slope \( m=\frac{9 - 12}{2 - 0}=\frac{-3}{2}=- 1.5 \). Ah, right, because if we go from \( (0,12) \) to \( (2,9) \), the change in y is \( 9 - 12=-3 \), change in x is \( 2 - 0 = 2 \), so \( m=\frac{-3}{2}=-1.5 \). So the slope is - 1.5 and the y - intercept \( b = 12 \). So the equation is \( y=-1.5x + 12 \), which is option d.

Answer:

d. \( y = -1.5x + 12 \)