a What similarities and differences do parallel have?
B
b What similarities and differences do perpendicular have?
A
a y=2x+12
B
b y=- 1/2x-1/2
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 2.
y=2x-3
If we write the desired equation in slope-intercept form, y=mx+b, we can add this slope.
y=2x+ b
To determine the value of b, we can use the fact that our line must pass through (- 5,2). Let's substitute x= - 5 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=2x-3 that passes through (- 5,2).
y=2x+ 12
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 - 12.
Given Slope:& m_1=2
Opposite Reciprocal:& m_2=- 12
With this information, we can write a general equation for all lines with slope perpendicular to that of the given equation.
y=- 1/2x+b
Once again, to find b, we can substitute x= - 5 and y= 2 into this equation.
