Question

write an equation of the line below.

Explanation:

Step1: Identify two points

From the graph, we can see two points on the line: \((-5, 3)\) and \((0, 0)\) (the y - intercept).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(-5,3)\), we have \(m=\frac{3 - 0}{-5 - 0}=\frac{3}{-5}=-\frac{3}{5}\)? Wait, no, wait. Wait, if we take \((x_1,y_1)=(-5,3)\) and \((x_2,y_2)=(0,0)\), then \(m=\frac{0 - 3}{0 - (-5)}=\frac{-3}{5}=-\frac{3}{5}\)? Wait, no, wait, let's check the graph again. Wait, the line passes through \((-5,3)\) and \((0,0)\)? Wait, no, when \(x = 0\), \(y=0\), and when \(x=-5\), \(y = 3\)? Wait, no, let's recalculate. Wait, the slope between \((-5,3)\) and \((0,0)\): \(m=\frac{0 - 3}{0 - (-5)}=\frac{-3}{5}=-\frac{3}{5}\)? Wait, but let's check another point. Let's take \((0,0)\) and \((5,-3)\), then \(m=\frac{-3 - 0}{5 - 0}=-\frac{3}{5}\). So the slope \(m =-\frac{3}{5}\)? Wait, no, wait, maybe I made a mistake. Wait, the line goes from \((-5,3)\) to \((0,0)\), so the change in \(y\) is \(0 - 3=-3\), change in \(x\) is \(0 - (-5)=5\), so slope is \(\frac{-3}{5}=-\frac{3}{5}\). And the y - intercept \(b\) is 0, since the line crosses the y - axis at \((0,0)\).

Step3: Write the equation

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We found \(m =-\frac{3}{5}\) and \(b = 0\), so the equation is \(y=-\frac{3}{5}x+0\), which simplifies to \(y =-\frac{3}{5}x\). Wait, but let's verify with the point \((-5,3)\). If \(x=-5\), then \(y=-\frac{3}{5}\times(-5)=3\), which matches. And when \(x = 0\), \(y = 0\), which also matches. So the equation of the line is \(y=-\frac{3}{5}x\).

Wait, but maybe I made a mistake in the slope. Wait, let's check the graph again. The line passes through \((-5,3)\) and \((0,0)\), so the slope is \(\frac{0 - 3}{0 - (-5)}=-\frac{3}{5}\), and the y - intercept is 0. So the equation is \(y=-\frac{3}{5}x\).

Answer:

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