Questions: Deja graphed the line below. Which equation could represent Deja's graph? a. y=4x-3 b. y=-3x+4 c. y=-5x d. y=-2x-1

Transcript text: Deja graphed the line below. Which equation could represent Deja's graph? a. $y=4 x-3$ b. $y=-3 x+4$ c. $y=-5 x$ d. $y=-2 x-1$

Solution

Solution Steps

Step 1: Find the y-intercept

The y-intercept is where the line crosses the y-axis. In the given graph, the line crosses the y-axis at y = 0.

Step 2: Calculate the slope

The slope is the change in y divided by the change in x. We can pick two points on the line to determine this. From the graph, when x = 0, y = 0 and when x = 1, y = -2. This implies that the change in y is -2 - 0 = -2, and the change in x is 1 - 0 = 1. So, the slope is -2/### Step 1: Identify the Slope of the Line

The graph shows a line with a negative slope, as it goes downwards from left to right.

Step 2: Compare the Slopes of the Given Equations

Option a: $ y = 4x - 3 $ has a positive slope of 4.
Option b: $ y = -3x + 4 $ has a negative slope of -3.
Option c: $ y = -5x $ has a negative slope of -5.
Option d: $ y = -2x - 1 $ has a negative slope of -2.

Step 3: Determine the Correct Equation Based on the Slope

Since the line in the graph has a negative slope, we can eliminate option a.
Among the remaining options (b, c, d), we need to match the slope of the line in the graph. The line appears to have a slope that is not as steep as -5 but steeper than -2.