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 -21.
GivenSlope:OppositeReciprocal:m1=2m2=-21
With this information, we can write a general equation for all lines with slope perpendicular to that of the given equation.
y=-21x+b
Once again, to find b, we can substitute x=-5 and y=2 into this equation.
Mathleaks uses cookies for an enhanced user experience. By using our website, you agree to the usage of cookies as described in our policy for cookies.