What similarities and differences do perpendicular lines have?
y=2x+3
Practice makes perfect
When lines are perpendicular their slopes will be opposite reciprocals of one another. With this, we know that all lines that are perpendicular to our given line will have a slope of 2.
Given Slope:& m_1=-1/2
Opposite Reciprocal:& m_2=2
With this information, we can write a general equation for all lines with a slope perpendicular to that of the given equation.
y= 2x+ b
To determine the value of b, we can use the fact that our line must pass through (0, 3). Note that we are given a point where the x-coordinate equals 0. Therefore, the y-intercept b of the line is 3. Now we have everything necessary to write the equation for the perpendicular line.
y=2x+ 3
