Question

write an equation of the line below. try again

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, 0)\) (the origin) and \((-2, 6)\) (the blue dot). Wait, no, actually, looking at the y-intercept, when \(x = 0\), \(y = 0\)? Wait, no, the line crosses the y-axis at \((0, 0)\)? Wait, no, let's check again. Wait, the blue dot is at \((-2, 6)\) and the line also passes through \((0, 0)\)? Wait, no, maybe I made a mistake. Wait, the y-intercept: when \(x = 0\), what's \(y\)? Looking at the graph, the line passes through \((0, 0)\) and \((-2, 6)\)? Wait, no, let's calculate the slope. Let's take two points: let's say \((0, 0)\) and \((-2, 6)\). Wait, no, the slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Wait, maybe another pair. Wait, the blue dot is at \((-2, 6)\) and when \(x = 0\), \(y = 0\)? Wait, no, let's see the grid. The x-axis is from -8 to 8, y-axis from -8 to 8. The blue dot is at \(x=-2\), \(y = 6\). And the line passes through \((0, 0)\)? Wait, no, when \(x = 0\), the line is at \(y = 0\)? Wait, no, maybe the y-intercept is 0? Wait, let's check the slope. Let's take two points: \((-2, 6)\) and \((0, 0)\). Then the slope \(m=\frac{0 - 6}{0 - (-2)}=\frac{-6}{2}=-3\). So the slope is -3. And the y-intercept \(b\) is 0, because when \(x = 0\), \(y = 0\). So the equation of the line is \(y = mx + b\), so \(y=-3x + 0\), which is \(y=-3x\). Wait, let's verify with the point \((-2, 6)\). Plug \(x=-2\) into \(y=-3x\): \(y=-3\times(-2)=6\), which matches. So that works.

Wait, maybe I misread the y-intercept. Let's check again. The line crosses the y-axis at \((0, 0)\), so \(b = 0\). The slope between \((-2, 6)\) and \((0, 0)\) is \(\frac{0 - 6}{0 - (-2)}=\frac{-6}{2}=-3\). So the equation is \(y=-3x\).

Step1: Find two points on the line

We identify two points: \((0, 0)\) (y-intercept) and \((-2, 6)\) (the blue dot).

Step2: Calculate the slope \(m\)

Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), where \((x_1, y_1)=(0, 0)\) and \((x_2, y_2)=(-2, 6)\).
\[
m=\frac{6 - 0}{-2 - 0}=\frac{6}{-2}=-3
\]

Step3: Determine the y-intercept \(b\)

The y-intercept \(b\) is the value of \(y\) when \(x = 0\). From the point \((0, 0)\), we see \(b = 0\).

Step4: Write the equation of the line

Using the slope-intercept form \(y = mx + b\), substitute \(m=-3\) and \(b = 0\):
\[
y=-3x + 0
\]
Simplifying, we get \(y=-3x\).

Answer:

\(y = -3x\)