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kcbrosell
find an equation for the line with the given properties Question: Perpendicular to the line x − 2y = −5; containing the point (0, 4)
so put that equation in this form: y=mx+b
so we can find the slope of the perpendicular line after we do that
Do you need help putting in that form?
1. Convert equation to y=mx+b, to find slope 2. Our second slope is the negative reciprocal of the given line's slope 3. Substitute the new slope, and the values of x and y into y=mx+b to solve for b (the y-int)
I am not understanding
Do you know how to write the equation given in this form: y=mx+b?
You are just trying to solve for y: \[x-2y=-5\] \[\text{ add } 2y \text{ on both sides }\] \[x-2y+2y=-5+2y\] \[x=-5+2y\] Now add 5 on both sides \[x+5=2y\] Now divide both sides by 2 \[\frac{x+5}{2}=y =>y=\frac{x}{2}+\frac{5}{2} =>\frac{1}{2}x+\frac{5}{2}\] so what is the slope here?
1/5=5 & 2/2=1, is that right
y=mx+b where is m is slope so what is in front of x up there? 1/2 right? so what is the slope of a perpendicular line to this one? in other words what satisfies this equation 1/2 * ? = -1
close -2 would be the slope of the perpendicular line
so we have all lines are in this form y=mx+b => this line has this form: y=-2x+b
now we know a point on the line (0,4)
where x=0 and y=4 so we have enough info to find b replace x with 0 and y with 4 4=-2(0)+b how do you solve this for b?
wouldnt you multiply each side by -4
4=0+b since -2(0)=0 4=b since 0+b=b
so the equation us y=-2x+4