SOLUTION: Find an equation for the line with the given properties. Express the answer using the slope-intercept form of the equation of a line. Parallel to the line y = -3x; containing t

Algebra ->  Graphs -> SOLUTION: Find an equation for the line with the given properties. Express the answer using the slope-intercept form of the equation of a line. Parallel to the line y = -3x; containing t      Log On


   

Question 991502: Find an equation for the line with the given properties. Express the answer using the slope-intercept form of the equation of a line.
Parallel to the line y = -3x; containing the point (2, 3)
a. y - 3 = -3x - 2
b. y = -3x - 9
c. y = -3x + 9
d. y = -3x
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Since any two parallel lines have the same slope we know the slope of the unknown line is -3 (its from the slope of y=-3%2Ax%2B0 which is also -3). Also since the unknown line goes through (2,3), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y-3=-3%2A%28x-2%29 Plug in m=-3, x%5B1%5D=2, and y%5B1%5D=3



y-3=-3%2Ax%2B%283%29%282%29 Distribute -3



y-3=-3%2Ax%2B6 Multiply



y=-3%2Ax%2B6%2B3Add 3 to both sides to isolate y

y=-3%2Ax%2B9 Combine like terms

So the equation of the line that is parallel to y=-3%2Ax%2B0 and goes through (2,3) is y=-3%2Ax%2B9


So here are the graphs of the equations y=-3%2Ax%2B0 and y=-3%2Ax%2B9



graph of the given equation y=-3%2Ax%2B0 (red) and graph of the line y=-3%2Ax%2B9(green) that is parallel to the given graph and goes through (2,3)



so, your answer is: c. y+=+-3x+%2B+9