We have been asked to describe two different methods we could use to graph the following equation.
y=2x+4
There are actually more than two methods, but let's consider the two most common ways.
First Method: We can begin by creating a table of values. Then, we can plot the points on the coordinate plane. Finally, we can connect the points. Note that it only takes two points and a straight edge to graph a line.
Second Method: We can use the slope-intercept form, y=mx+b. In this form, m is the slope and b is the y-intercept. We can plot the y-intercept and use the slope to find a second point. Then, we can connect the two points.Let's apply both methods and decide which one we prefer.
First Method
We will begin by forming a table of values for the equation y=2x+4.
x
2x+4
y
- 3
2( - 3)+4
- 2
- 2
2( - 2)+4
0
- 1
2( - 1)+4
2
0
2( 0)+4
4
1
2( 1)+4
6
We will plot these ordered pairs on a coordinate plane and connect them with a line.
Let's now apply the second method.
Second Method
Notice that the given equation y=2x+4 is in slope-intercept form, y=mx+b, where the slope m is 2 and the y-intercept b is 4. If we rewrite the slope m= 2 as a fraction, it becomes 21.
m=rise/run ⇒ m=2/1
Since we know that the equation intercepts the y-axis at (0, 4), we will travel 1 step to the right and 2 steps up from there to find another point. Finally, we draw a line that passes through the points.
While the method you prefer is totally up to you, we prefer using the slope-intercept form. It is faster and more reliable.
