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Question 227030: write an equation of the line containing the given point and parallel to the given line. (7,9); 8x-9y=5
Answer by algebrapro18(249)   (Show Source):
You can put this solution on YOUR website! Well first we need to solve the given equation for y so we know its slope. I'll leave the algebra for you to do but the final answer is y = 8/9x-5/9. So we know that the slope is 8/9. We also know that parallel lines have the same slope so our line will have slope 8/9. Now there are 2 ways to solve this problem from here.
Method 1. Using Slope-intercept form
we know that the equation for a line in slope-intercept form is y=mx+b where m is the slope of the line and x and y are points on the line. Since we know a point on our line and the slope of our line we can just plug in and solve for b.
y = mx+b
9 = 8/9(7)+b
I'll leave the algebra to you but you should end up with b = 25/9. So our equation will be y = 8/9x+25/9.
Method 2. Using Point-Slope form.
There is another equation you can use to find the equation of a line, its y-y1=m(x-x1) where (x1,y1) is a point on the line and m is the slope. Since we know a point and a slope we can just plug into this formula.
y-9=8/9(x-7)
Doing the algebra you will see that you end up with y = 8/9x+25/9 which is what we got above.
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