Find the equation of the line that is perpendicluar to y=-2/3x and contains the point (4,-8)
1 answer:
Answer:
Step-by-step explanation:
The slope of two perpendiculars is
m1*m2 = - 1
m1 = - 2/3
-2/3 * m2 = -1 Multiply both sides by -3/2
-3/2 * -2/3 * m2 = -1*-3/2
m2 = 3/2
So far what you have is
y = 3/2 x + b
x = 4
y = - 8
-8 = 3/2*4 + b
-8 = 6 + b Subtract 6 from both sides
b = - 14
Complete line
y = 3/2 x - 14
The red line is y = -2/3x
The blue line is y = 3/2x - 14
The point (4,-8) is marked for you
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The solution is shown in the graph attached.
Explanation:
I am goind to teach you how to get that solution.
1) Restricctions: both x and y cannot be negative, i.e. x ≥ 0 and y ≥ 0
⇒ the solution is on the first quadrant.
2) Using the prices of the tickets, $ 8 for adults, and $ 6 for children, the linear equation for the costs is: cost = 8x + 6y.
3) Since the radio station is willing to spend a maximum of $ 172 you have the final restriction:
⇒ 8x + 6y ≤ 172.
4) Then the solutions that meet the three restrictions (x ≥0, y ≥ 0, and 8x + 6y ≤ 172) is found graphically by drawing the line 8 x + 6y = 172
5) To draw the line 8x + 6y = 172, use the axis intercepts:
x = 0 ⇒ y = 172/6 = 86/3 ⇒ point (0, 86/3)
y = 0 ⇒ x = 172/8 = 86/4 ⇒ point (86/4, 0)
6) Once you have the line you shade the region that is between the line and the two axis. That region contain of the possible solutions.
Explanation:
I am goind to teach you how to get that solution.
1) Restricctions: both x and y cannot be negative, i.e. x ≥ 0 and y ≥ 0
⇒ the solution is on the first quadrant.
2) Using the prices of the tickets, $ 8 for adults, and $ 6 for children, the linear equation for the costs is: cost = 8x + 6y.
3) Since the radio station is willing to spend a maximum of $ 172 you have the final restriction:
⇒ 8x + 6y ≤ 172.
4) Then the solutions that meet the three restrictions (x ≥0, y ≥ 0, and 8x + 6y ≤ 172) is found graphically by drawing the line 8 x + 6y = 172
5) To draw the line 8x + 6y = 172, use the axis intercepts:
x = 0 ⇒ y = 172/6 = 86/3 ⇒ point (0, 86/3)
y = 0 ⇒ x = 172/8 = 86/4 ⇒ point (86/4, 0)
6) Once you have the line you shade the region that is between the line and the two axis. That region contain of the possible solutions.