SOLUTION: Use the given conditions to write an equation for the line in the indicated form. Passing through (5, -3) and parallel to the line whose equation is y = -3x + 9; slope-intercep

Algebra ->  Linear-equations -> SOLUTION: Use the given conditions to write an equation for the line in the indicated form. Passing through (5, -3) and parallel to the line whose equation is y = -3x + 9; slope-intercep      Log On


   

Question 180809: Use the given conditions to write an equation for the line in the indicated form.
Passing through (5, -3) and parallel to the line whose equation is y = -3x + 9;
slope-intercept form
Found 4 solutions by jim_thompson5910, eperette, mgmoeab, sanjoy259:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

We can see that the equation y=-3%2Ax%2B9 has a slope m=-3 and a y-intercept b=9.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=-3.
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=-3 and the coordinates of the given point .


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


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


y%2B3=-3%28x-5%29 Rewrite y--3 as y%2B3


y%2B3=-3x%2B-3%28-5%29 Distribute


y%2B3=-3x%2B15 Multiply


y=-3x%2B15-3 Subtract 3 from both sides.


y=-3x%2B12 Combine like terms.


So the equation of the line parallel to 3x%2By=9 that goes through the point is y=-3x%2B12.


Here's a graph to visually verify our answer:
Graph of the original equation y=-3%2Ax%2B9 (red) and the parallel line y=-3x%2B12 (green) through the point .

Answer by eperette(173) About Me  (Show Source):
You can put this solution on YOUR website!
Concepts you should know:
1) Parallel lines have equal slopes
2) Equation in slope-intercept form: y=mx+b; where m=slope and b=y-intercept
3) Given a point and slope, you will need to use point-slope form to start....
4) Point-Slope Form: y-y1= m (x - x1)
Answer:
(x1, y1) = (5, -3)
m= -3
y-y1= m(x-x1)
y--3 = -3(x-5)
y+3 = -3(x-5)
y+3 = -3(x)-3(-5)
y+3 = -3x + 15
y+3-3 = -3x + 15 -3
y= -3x + 12

Answer by mgmoeab(37) About Me  (Show Source):
You can put this solution on YOUR website!
POINT-INTERCEPT FORM = y= mx+ b
...
If the line is parallel to y = -3x + 9, then the lines have THE SAME slope. In this case, the slope is m= -3
...
To find the equation of the line, you need to use:
POINT-SLOPE FORM = Y- y = m(X -x)
The given point for which the line passes through is P(5, -3)
The slope of the line is m = -3
Then the equation of the line is given by
Y - (-3) = -3 (X - (5) ---> y + 3 = -3(X -5)
If they ask you to put it in point- intercept for, then you just have to solve for 'y'
...
y= -3X + 12 <--

Answer by sanjoy259(2) About Me  (Show Source):
You can put this solution on YOUR website!
EASY WAY!!!!!!!!!!!!!! NEED TO REMEMBER ONLY ONE FORMULA

let see what i know xy=(5,-3) Slope = -3 FROM y = -3x + 9 PARALLEL EQUATION

ALWAYS HAVE SAME SLOPE(M)

take the x=5 and y= -3 that is given and also we know the slope(M)= -3
y = mx + b
y = -3x + b
-3 = -3(5) + b
-3 = -15 + b
+15 +15
------------
12 = b
lets take the same formula again Y = mx + b and plug in slope(M) and the B
y = mx + b
y = -3x + 12 -- the answer