QM Q6.) Write the slope-intercept equation of the function f whose graph satisifies the given conditions.

Mathematics

1 answer:

vichka [17]3 years ago

6 0

Greetings!

The equation of a line in slope-intercept form is:

y = mx + b

m is the slope
b is the y- intercept

What we need to do is to re-arrange 2x - 9y - 18 = 0. We wanna make it looks like y = mx + b

So, the equation is:

2x - 9y - 18 = 0

Subtract 2x - 18 from both sides

→ -9y = -2x + 18

Since we want y, we need to divide both sides by -9

$\frac{-9y}{-9} = \frac{-2x + 18}{-9}$

Thus,

y = 2/9 x - 2 which is in the slope intercept form

Slope m = 2/9 and the y-intercept is = - 2

Given a line with slope m then the slope of a line perpendicular is:

$m_{perpendicular} = - \frac{1}{m}$

$m_{perpendicular} = - \frac{1}{2/9 }$ = - 9/2

Thus,

The equation of the function is:

$y = - \frac{9}{2} x - 2$

Let me know if you have questions about the answer. As always, it is my pleasure to help students like you!

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Differentiate both sides with respect to x

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3 years ago

Akira is a salon owner. Yesterday, she did 2 haircuts and colored the hair of 1 client, charging a total of $194. Today, she did

joja [24]

Answer:

$\boxed {\boxed {\sf Haircut: \$47 \ and \ Color: \$ 100}}$

Step-by-step explanation:

Let's set up a system of equations. (1 equation for yesterday and 1 for today).

Let h = haircut and c= color

$2h+1c= 194$ (Yesterday: 2 haircuts and 1 color for $194).

$2h+4c= 494$ (Today: 2 haircuts and 4 colors for $494).

Notice that both equations have a 2h. If we subtract the two equations, the 2h will cancel and leave us with one variable, c.

$\ \ (2h+1c=194) \\- (2h+4c=494)$

$\ \ 1c=194 \\- (4c=494)$

$-3c= -300$

Since we are solving for c, we must isolate the variable. It is being multiplied by -3. The inverse of multiplication is division. Divide both sides by -3.

$-3c/-3=-300/-3 \\c= -300/-3 \\c=100$