What is the equation of a line that is perpendicular to −x+3y=9 and passes through the point (−3, 2) ?
1 answer:
Answer
the equation of a line that is perpendicular to −x+3y=9 is y=-3x-7
Step-by-step explanation:
Equation of given line is −x+3y=9
we write the equation in y =mx+b to find slope of given line (m)
−x+3y=9
Add x on both sides
3y = x+ 9
Divide by 3 on both sides
Slope of given line = 1/3
Slope of perpendicular line is the negative reciprocal of slope of given line
Slope of perpendicular line = -3
Perpendicular line passes through point (-3,2) that is (x1,y1)
Now we use point slope equation
y - y1 = m (x-x1)
y - 2 = -3(x-(-3))
y - 2= -3(x+3)
y -2 = -3x -9
Add 2 on both sides
y = -3x - 7
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Answer:
The two points solutions to the system of equations are: (2, 3) and (-1,6)
Step-by-step explanation:
These system of equations consists of a parabola and a line. We need to find the points at which they intersect:
Since we were able to factor out the quadratic expression, we can say that the x-values solution of the system are:
x = 2 and x = -1
Now, the associated y values we can get using either of the original equations for the system. We pick to use the linear equation for example:
when x = 2 then
when x= -1 then
Then the two points solutions to the system of equations are: (2, 3) and (-1,6)