What similarities and differences do parallel lines have?
B
b
What similarities and differences do perpendicular lines have?
A
a
y=3x-5
B
b
y=- 1/3x-5/3
Practice makes perfect
a
When lines are parallel, they have the same slope. With this, we know that all lines that are parallel to our given line will have a slope of 3.
y=3x+2
If we write the desired equation in slope-intercept form, y=mx+b, we can add this slope.
y=3x+ b
To determine the value of b, we can use the fact that our line must pass through (1,- 2). Let's substitute x= 1 and y= - 2 into the equation and solve for b.
Now that we have the y-intercept, we can conclude the line parallel to y=3x+2 that passes through (1,- 2).
y=3x+( -5) ⇔ y=3x-5
b
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 - 13.
Given Slope:& m_1=3
Opposite Reciprocal:& m_2=- 13
With this information, we can write a general equation for all lines with slope perpendicular to that of the given equation.
y=- 1/3x+b
Once again, to find b, we can substitute x= 1 and y= - 2 into this equation.
