Question

How do you draw the line with the slope `m=1/2` and `y`- intercept `5`?

Answer 1

Start at the y-intercept and count `"rise"/"run"` for the slope.

Explanation:

The equation of the line is `y = 1/2x+5`

You know that the `y`-intercept is at `5`. This is the point where the line crosses the `y`-axis.

Slope is defined as `"y-change"/"x-change" = "vertical"/"horizontal"`

Slope = `1/2` means `2` y units for each `1` x unit.

Starting from the y-intercept at 5:
count UP 1 unit and RIGHT 2 units, mark a point. `(2,6)`
Repeat this process, marking marking points up and to the right.

Starting from the y-intercept at 5:
count DOWN 1 unit and LEFT 2 units, mark a point. `(-2,4)`
Repeat this process, marking marking points down and to the left.

Join the points with a straight line.

graph{1/2x+5 [-19.73, 20.27, -7.08, 12.92]}

Answer 2

`y = 1/2x + 5`

Explanation:

Standard form of an equation of a line is `y = mx + b` where `m` = slope = `(y_2 - y_1)/(m_2 - m_1)` and `b` is the `y`-intercept, which is the point `(0, b)`

Start by plotting the `y`-intercept `(0, 5)`

The slope `m = 1/2`. From the `y`-intercept `(0, 5)`, go up `1, (+y)` and over `2, (+x)` and place a point. Draw a line that passes through the two points.

graph{y = 1/2x + 5 [-9.29, 10.71, 1.32, 11.32]}