Y - y1 = m( x - x1); where m = (y2 - y1)/(x2 - x1);
We have m = (6-0)/(7-5) = 6 / 2 = 3 ;
The equation of the line is: y - 0 = 3(x-5);
Finally: y = 3x - 15.
First, let's convert each line to slope-intercept form to better see the slopes.
Isolate the y variable for each equation.
2x + 6y = -12
Subtract 2x from both sides.
6y = -12 - 2x
Divide both sides by 6.
y = -2 - 1/3x
Rearrange.
y = -1/3x - 2
Line b:
2y = 3x - 10
Divide both sides by 2.
y = 1.5x - 5
Line c:
3x - 2y = -4
Add 2y to both sides.
3x = -4 + 2y
Add 4 to both sides.
2y = 3x + 4
Divide both sides by 2.
y = 1.5x + 2
Now, let's compare our new equations:
Line a: y = -1/3x - 2
Line b: y = 1.5x - 5
Line c: y = 1.5x + 2
Now, the rule for parallel and perpendicular lines is as follows:
For two lines to be parallel, they must have equal slopes.
For two lines to be perpendicular, one must have the negative reciprocal of the other.
In this case, line b and c are parallel, and they have the same slope, but different y-intercepts.
However, none of the lines are perpendicular, as -1/3x is not the negative reciprocal of 1.5x, or 3/2x.
<h3><u>B and C are parallel, no perpendicular lines.</u></h3>
Answer:
Patricia spent $24 on presents, while Donald spent $12 and Carl spent $36.
Step-by-step explanation:
The problem is to solve how much money each person spent on presents in the year, through a series of equivalences. In order to determine how much money each one spent, the following equation must be proposed:
Patricia = X
Donald = 1 / 2X
Carl = 3/2 X
X + 1 / 2X + 3 / 2X = 72
1X + 0.5 X + 1.5 X = 72
3X = 72
X = 72/3
X = 24
Thus, Patricia spent $ 24 on presents, while Donald spent $ 12 (2/24) and Carl spent $ 36 (1.5 x 24).
Answer:
14 more pounds
Step-by-step explanation:
32-18
