First we will graph the linear function y=2x-1. Then we will graph one line that is parallel to it. After that we will graph a line that is perpendicular to the first line.
Graphing y=2x-1
To graph the line y=2x -1, we plot a point at the y-intercept (0, - 1).
Since the line is given in slope-intercept form, we can identify its slope in the equation.
y= 2x-1 ⇒ m= 2
If we use the line's slope, we can plot a second point that the line passes through.
m=2=2/1
⇕
Δ y/Δ x=2/1
By going 1 step horizontally and 2 steps vertically, we end up on another point on the line.
By drawing a line through both points we find the graph of our function.
Graphing a Parallel Line
Parallel lines have the same slope but different y-intercepts. In other words, the parallel line we are looking for will be in the following form.
y=2x+ b, where b≠- 1
Let's arbitrarily pick a y-intercept of - 4. Now we can graph the line y=2x -4 in the same way we did with the original line.
Graphing a Perpendicular Line
Perpendicular lines have slopes which are negative reciprocals of each other.
m_1* m_2=- 1
We can determine the slope m_2, by substituting the slope of the original line m_1 into the formula and solving for m_2.
There is no restriction as to what y-intercept a perpendicular line can have. Therefore, we can arbitrarily pick b= 4. Let's now write the equation of our perpendicular line.
y=- 1/2x+ 4
Let's graph it in the same coordinate plane. When we graph it we keep in mind that since we have a negative slope we make the vertical step down.
