Question

the graph shows a linear relationship. write an equation for the line in slope - intercept form.

Explanation:

Step1: Identify slope-intercept form

Slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Find the y - intercept ($b$)

The line passes through the origin $(0,0)$, so $b = 0$.

Step3: Calculate the slope ($m$)

We can use two points on the line. Let's take $(0,0)$ and $(1,2)$ (from the graph, when $x = 1$, $y = 2$). The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting the points $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(1,2)$ into the formula, we get $m=\frac{2 - 0}{1 - 0}=2$. We can also check with another pair of points, say $(2,4)$: $m=\frac{4 - 0}{2 - 0}=2$.

Step4: Write the equation

Substitute $m = 2$ and $b = 0$ into the slope - intercept form $y=mx + b$. We get $y = 2x+0$, which simplifies to $y = 2x$.

Answer:

$y = 2x$