Question

1. graph the line that has a slope of \\(\frac{1}{2}\\) and includes the point (2, 1). 2) click to select points on the graph.

Explanation:

Step1: Recall the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line. Here, $m = \frac{1}{2}$ and $(x_1,y_1)=(2,1)$. Substituting these values into the point - slope form, we get $y - 1=\frac{1}{2}(x - 2)$.

Step2: Simplify the equation

Expand the right - hand side: $y - 1=\frac{1}{2}x-1$. Then, add 1 to both sides of the equation. We have $y=\frac{1}{2}x$.

Step3: Find other points on the line

We know that the slope $m=\frac{\text{rise}}{\text{run}}=\frac{1}{2}$. Starting from the point $(2,1)$, if we move 2 units to the right (increase $x$ by 2, so $x = 2 + 2=4$) and 1 unit up (increase $y$ by 1, so $y=1 + 1 = 2$), we get the point $(4,2)$. If we move 2 units to the left (decrease $x$ by 2, so $x=2-2 = 0$) and 1 unit down (decrease $y$ by 1, so $y = 1-1=0$), we get the point $(0,0)$.
To graph the line, we can plot the points $(0,0)$, $(2,1)$, $(4,2)$ and draw a straight line through them.

Answer:

To graph the line, plot the points \((0,0)\), \((2,1)\), \((4,2)\) (and other points found using the slope \(\frac{1}{2}\)) and draw a straight line passing through them. The equation of the line is \(y=\frac{1}{2}x\).