Questions: Let x be the profit of a company and let y be the amount the company owner makes, both in thousands of dollars. The graph shows the relationship between x and y. Which equation describes this relationship? (A) y=x-3 (B) y=5x (C) y=0.6x (D) y=x+5

Let x be the profit of a company and let y be the amount the company owner makes, both in thousands of dollars. The graph shows the relationship between x and y. Which equation describes this relationship?
(A) y=x-3
(B) y=5x
(C) y=0.6x
(D) y=x+5

Transcript text: Let $x$ be the profit of a company and let $y$ be the amount the company owner makes, both in thousands of dollars. The graph shows the relationship between $x$ and $y$. Which equation describes this relationship? (A) $y=x-3$ (B) $y=5 x$ (C) $y=0.6 x$ (D) $y=x+5$

Solution

Solution Steps

Step 1: Find two points on the line

Two points that lie on the line are (0,0) and (5,3).

Step 2: Calculate the slope

The slope of the line is given by the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$. Using the points (0,0) and (5,3), the slope is $m = \frac{3 - 0}{5 - 0} = \frac{3}{5} = 0.6$.

Step 3: Determine the y-intercept

The y-intercept is the point where the line crosses the y-axis. In this case, the line crosses the y-axis at the origin (0,0), so the y-intercept is 0.

Step 4: Write the equation

Since the slope is 0.6 and the y-intercept is 0, the equation of the line is $y = 0.6x$.