Question

Graph the line y=1/3x+2 on the coordinate plane at the left

Answer 1

ANSWER and EXPLANATION

We want to plot the line represented by the equation:

`y\text{ = }(1)/(3)x\text{ + 2}`

where slope = 1/3

y intercept = 2

The quickest way to plot this graph is to get at least two coordinate points from the equation and then join them.

The first coordinate point we can use is the y intercept.

The y intercept is the value of y when x is 0. This means that the coordinate point of the y intercept is (0, 2)

Now, that we have one point, we can get another by using the slope.

Slope is defined as the vertical rise divided by the horizontal run, which means that from any point on the graph, if we add the rise to the y coordinate and the run to the x coordinate, we will get another point on the graph.

The slope is:

`\text{slope = }(rise)/(run)\text{ = }(1)/(3)`

So: rise = 1; run = 3

Therefore, adding that to the y intercept, we have:

(0 + 3, 2 + 1) => (3, 3)

Now, we have two points (0, 2) and (3, 3)

Let us plot the graph:

That is the graph of the line.