Question

which equation represents the line shown in the graph? a. $y = -\frac{3}{5}x$ b. $y = -\frac{5}{3}x$ c. $y = \frac{5}{3}x$ d. $y = \frac{3}{5}x$

Explanation:

Step1: Determine the slope formula

The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify two points on the line

From the graph, the line passes through the origin \((0,0)\) and another point, say \((5, - 3)\) (by observing the grid, moving 5 units right and 3 units down from the origin).

Step3: Calculate the slope

Using the two points \((0,0)\) and \((5, - 3)\), substitute into the slope formula: \( m=\frac{-3 - 0}{5 - 0}=\frac{-3}{5}=-\frac{3}{5} \).

Step4: Determine the equation of the line

Since the line passes through the origin \((0,0)\), the y - intercept \( b = 0 \). The equation of a line in slope - intercept form is \( y=mx + b \). Substituting \( m =-\frac{3}{5}\) and \( b = 0 \), we get \( y=-\frac{3}{5}x \).

Answer:

A. \( y = -\frac{3}{5}x \)