SOLUTION: What is the answer to these problems: find the slope-intercept form of the question whose graph passes through (1,4) and is parallel to a line whose equation is y=3x+5 and find the

Algebra ->  Equations -> SOLUTION: What is the answer to these problems: find the slope-intercept form of the question whose graph passes through (1,4) and is parallel to a line whose equation is y=3x+5 and find the      Log On


   

Question 12728: What is the answer to these problems: find the slope-intercept form of the question whose graph passes through (1,4) and is parallel to a line whose equation is y=3x+5 and find the slope-intercept form of the equation whose graph passes through (0,5) and is perpendicular to the line whose equation is y=6x-4
Answer by AdolphousC(70) About Me  (Show Source):
You can put this solution on YOUR website!
Your first question, a line parallel to y = 3x + 5 passing through (1,4)
If two lines are parallel they have the same slope.
We know we want our line to have the form y = mx + b.
We know our slope HAS to be 3 becasue the lines are parallel
So now we have y = 3x + b use your point to solve for b
+y+=+3x+%2B+b+ Substitute
4+=+3%281%29+%2B+b+ Multiply
+4+=+3+%2B+b+ Subtract 3 from both sides
+1+=+b+
So we know our slope is 3 and y intercept is 1 so
y = 3x + 1 is parallel to y = 3x + 5


Your next question, a line perpendicular to y = 6x - 3 passing through (0,5)
If two lines are perpendicular thier slopes are NEGATIVE RECIPROCALS
We know we want our line to have the form y = mx + b
We know our slope for our Perpendicular line is ( -1/6 )
So now we have
+y+=+%28-1%2F6%29x+%2B+b+ Using your point ( 0,5 ) to solve for b
+5+=+%28-1%2F6%29%280%29+%2B+b+ Simplify
+5+=+b+
We know our slope is ( -1/6 ) and our y intercept is 5 so
y = ( -1/6 )x + 5 is Perpendicular to y = 6x - 3