Question

1. a line passes through the origin and has a slope of draw the line by plotting any two points on the line.

Explanation:

Step1: Recall the slope-intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Since the line passes through the origin $(0,0)$, the y - intercept $b = 0$. Let's assume the slope $m=\frac{1}{2}$ (from the visible part of the problem). So the equation of the line is $y=\frac{1}{2}x$.

Step2: Find two points on the line

• For $x = 0$: Substitute $x = 0$ into $y=\frac{1}{2}x$. Then $y=\frac{1}{2}(0)=0$. So one point is $(0,0)$ (the origin).
• For $x = 2$: Substitute $x = 2$ into $y=\frac{1}{2}x$. Then $y=\frac{1}{2}(2) = 1$. So another point is $(2,1)$.

To draw the line, we plot the points $(0,0)$ and $(2,1)$ (or any other two points obtained from the line equation) and then draw a straight line through them.

Answer:

To draw the line:

1. Plot the point $(0,0)$ (the origin) since the line passes through it.
2. Use the slope $\frac{1}{2}$ (rise over run, which means for a run of 2 units (change in $x$), the rise is 1 unit (change in $y$)). Starting from $(0,0)$, move 2 units to the right (increase $x$ by 2) and 1 unit up (increase $y$ by 1) to get the point $(2,1)$.
3. Draw a straight line through the points $(0,0)$ and $(2,1)$.