SOLUTION: Please help me solve the following problem; Write the eqation of the line that passes through the point?(2,1) and is parallel to the line with the eqation y=5/2x + 6. I honestly do

Algebra ->  Coordinate-system -> SOLUTION: Please help me solve the following problem; Write the eqation of the line that passes through the point?(2,1) and is parallel to the line with the eqation y=5/2x + 6. I honestly do      Log On


   

Question 51380: Please help me solve the following problem; Write the eqation of the line that passes through the point?(2,1) and is parallel to the line with the eqation y=5/2x + 6. I honestly do not know where to even begin on this.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let's write the required equation of the line in the "slope-intercept" form: y+=+mx%2Bb Where: m is the slope of the line and b is the y-intercept of the line.
Remember that parallel lines have the same slope.
So, your new line is parallel the the line whose equation is:
y+=+%285%2F2%29x%2B6 Comparing this with the slope-intercept form:
y+=+mx%2Bb you can see that the slope of this line is m+=+5%2F2 and, because the new line is parallel to this, it too will have a slope of m+=+5%2F2.
So, step 1, for the new line, you can write:
y+=+%285%2F2%29x+%2B+b Now all you need to do is to find the value of b, the y-intercept of the new line.
You can do this by substituting the x- and y-coordinates of the given point (2, 1) into the equation y+=+%285%2F2%29x+%2B+b and solve for b.
1+=+%285%2F2%29%282%29+%2B+b Simplify this.
1+=+5+%2B+b Subtract 5 from both sides of the equation.
-4+=+b You can write the final equation now that you have the slope m+=+5%2F2 and the y-intercept b+=+-4:
y+=+%285%2F2%29x+-+4 ...and that's it!