Question

look at this graph: write the equation of the line.

Explanation:

Step1: Identify slope and y - intercept

Since there is no line shown, assume the line passes through the origin $(0,0)$ and we need a general - form for a non - vertical line $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. If the line is the x - axis, $m = 0$ and $b = 0$, and the equation is $y=0$. If the line is the y - axis, the equation is of the form $x = 0$ (but this is not in the $y=mx + b$ form). Let's assume a non - vertical and non - horizontal line passing through the origin. The slope $m$ can be calculated using two points $(x_1,y_1)$ and $(x_2,y_2)$ as $m=\frac{y_2 - y_1}{x_2 - x_1}$. Since the line passes through $(0,0)$ and another point $(x,y)$, $m=\frac{y - 0}{x - 0}=\frac{y}{x}$ (for $x
eq0$), and the equation of the line in slope - intercept form is $y=mx$. If the line is the x - axis (a horizontal line with all $y = 0$ values), the equation is $y = 0$.

Step2: Write the equation

The most general non - vertical line passing through the origin has the equation $y = mx$. But if we assume the x - axis (a common line on a coordinate graph), the equation of the line is $y = 0$.

Answer:

$y = 0$