Determine the slope of the lines parallel and perpendicular to -4x+3y=11
2 answers:
Answer:
and -
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
- 4x + 3y = 11 ( add 4x to both sides )
3y = 4x + 11 ( divide all terms by 3 )
y = x +
← in slope- intercept form
with slope m =
Parallel lines have equal slopes, thus
slope of parallel line =
Give a line with slope m then the slope of a line perpendicular to it is
= -
= -
= -
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Part A:
The first thing you should do is to graph both lines. Notice that one is of positive slope and another of negative slope.
The solution of the inequation system is given by the shaded region. That is, all the points that are in the shaded region satisfy the system of inequations.
Part B:
the point (-2, -2) is NOT included in the solution area (it is not in the shaded region.
Mathematically it is demonstrated by substituting inequalities and seeing that they are not satisfied
inequality 1
-2 <4 (-2) - 2
-2 <-10 (false)
inequality two
-2> = - (5/2) (- 2) - 2
-2> = 3 (false).
The first thing you should do is to graph both lines. Notice that one is of positive slope and another of negative slope.
The solution of the inequation system is given by the shaded region. That is, all the points that are in the shaded region satisfy the system of inequations.
Part B:
the point (-2, -2) is NOT included in the solution area (it is not in the shaded region.
Mathematically it is demonstrated by substituting inequalities and seeing that they are not satisfied
inequality 1
-2 <4 (-2) - 2
-2 <-10 (false)
inequality two
-2> = - (5/2) (- 2) - 2
-2> = 3 (false).