Solve y = -1/2x + 6 create an equation of a line parallel and perpendicular to this line that goes
1 answer:
Answer:
y = -½x + 12; y = 2x + 2
Step-by-step explanation:
1. <em>Solve the equation </em>
y = -½x + 6
(a) Let x = 0
y = -½(0) + 6
y = 0 + 6
y = 6
(b) Let y = 0
0 = -½x + 6 Subtract 6 from each side
-6 = -½x Multiply each side by -2
x = 12
The line passes through the points (0, 6) and (12, 0).
2. <em>Equation for parallel line </em>
The line passes through (4, 10).
y = mx + b
m = -½
10 = -½(4) + b
10 = -2 + b Add 1 to each side
b = 12
The equation for the parallel line is y = -½x + 12.
3. <em>Equation for perpendicular line </em>
(a). Find the <em>slope (m₁) of the original line </em>
The equation for the original line is
y = -½x + 6
slope = m₁ = -½
(b). Find the<em> slope (m₂) of the perpendicular line </em>
m₂ = -1/m₁ Substitute the value of m₁
m₂ = 2
(c). Find the <em>equation for the perpendicular line </em>
y = mx + b Substitute the value of m₂
y = 2x + b
The line passes through (4,10).
10 = 2 × 4 + b
10 = 8 + b Subtract 8 from each side
b = 2
y = 2x + 2
In the image, below, the red line is the graph of your original equation.
The green line passing through (4, 10) is the parallel line.
The black line passing through (4, 10) is the perpendicular line.
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The given ratio can be written in fraction form as
In order to find the rate, we need to divide 456 by 8, because it would give the unit value.
When we divide 456 by 8, we first take multiple of 8 closer to the number 45.
8*6=48 but it's greater than 45, so we would take 8*5 =40.
Subtracting 40 from 45, we get 5.
Getting 6 down, we get 56. Take multiple of 8 upto 56.
8*7= 56.
56 -56=0.
So, on dividing 456 by 8 we got 57.
Therefore, rate is 57 per unit.
