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3 years ago

Does anybody understand writing equations in slope intercept form?

Mathematics

2 answers:

irakobra [83]3 years ago

6 0

Hello!

Explanation: The y-intercept is the point on a graph at which the graph crosses the y-axis.

Slope-Intercept Form: y=mx+b

Let m represent the slope.

(0¹,b¹) (x²,y²)

m=rise/run=y-b/x-0

x(m)=y-b/x)x

mx=y-b

+b +b

mx+b=y

And switch sides of an equation.

y=mx+b

Hope this helps!

aleksandr82 [10.1K]3 years ago

4 0

slope intercept form

y=mx+b

where m is the slope and b is the y intercept

if we change from point slope form

y-y1 = m(x-x1)

we distribute

y-y1 = mx -x*x1

then add y1 to each side

y = mx -x*x1+y1

remember x and y are variables and should stay in the equation

m,x1,y1 are numbers from the problem

you may have to calculate the slope (m) from the formula

m = (y2-y1)/(x2-x1) from two points on the line

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(x^2+5)=7 and (x^2+5)k=21, what is the value of k?

Roman55 [17]

Step-by-step explanation:

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3 years ago

Describe the transformation of f(x) = sin x to g(x) = sin x - 17

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Answer: To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

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Cyndee is taking her siblings out for dessert. Ice cream, c, costs $4.00 per cone. Brownies, b, are $2.00 each. Water for everyo

GalinKa [24]

Answer:

The term that represent the amount of money she will spend on brownies is 2b

Step-by-step explanation:

Let

c ----> the number of cones

b ----> the number of brownies

we know that

The cost of desserts can be found using the expression

$4c+2b+5$

where

4c ----> is the term that represent the amount of money spend in cones

2b ----> is the term that represent the amount of money spend in brownies

5 ----> is the term that represent the amount of money spend in water

therefore

The term that represent the amount of money she will spend on brownies is 2b

That means ---> the number of brownies (b) multiplied by the cost of each brownie ($2)

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3 years ago

A classroom will seat 80 people. If 56 seats are filled, what percentage of the seats are filled?

PolarNik [594]

Divide the seats filled by the total amount of seats of the classroom.

$\frac{56}{80} = 0.7$

Multiply this result by 100 to find the percentage.

$0.7 * 100 = 70$

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3 years ago

Log_(5)(x-4)=1-log_(5)(x-8)

hjlf

Answer:

x = 3, x = 9

Step-by-step explanation:

When solving this problem, keep the general format of a logarithm in mind:

$b^x=y\\log_b(y)=x$

Where, (b) represents the base, (x) is the exponent, and (y) is the evalutaor. Please note that others might use slightly different terminotoly than what is used in this answer.

One is given the following expression, and is asked to solve for the parameter (x);

$log_5(x-4)=1-log_5(x-8)$

First, manipulate the exquestion such that all of the logarithmic expressions are on one side. Use inverse operations to do this.

$(log_5(x-4))+(log_5(x-8))=1$

Now use the Logarithmic Base Change rule to simplify. The Logarithmic Base Change rule states the following;

$log_b(x)=\frac{log(x)}{log(b)}$

Remember, if no base is indicated in a logarithm, then the logarithm's base is (10). Apply the Logarithmic Base Change rule to this problem;

$\frac{log(x-4)}{log(5)}+\frac{log(x-8)}{log(5)}=1$

Now remove the denominator. Multiply all terms in the equation by the least common denominator; ( $log(5)$ ) to remove it from the denominator on the left side.

$(\frac{log(x-4)}{log(5)}+\frac{log(x-8)}{log(5)}=1)*(log(5))$

$log(x-4)+log(x-8)=log(5)$

All logarithms have the same base, the left side of the equation has the addition of logarithms. This means that one can apply the Logarithm product rule. The logarithm product rules the following;

$log_b(x*y)=(log_b(x))+(log_b(y))$

This rule can be applied in reverse to simplify the left side of the equation. Rather than rewriting the product of logarithms as two separate logarithms being added, one can rewrite it as one logarithm getting multiplied.

$log(x-4)+log(x-8)=log(5)$

$log((x-4)(x-8))=log(5)$

Now used inverse operations to bring all of the terms onto one side of the equation:

$log((x-4)(x-8))=log(5)$

$log((x-4)(x-8))-log(5)=0$

Similar to the Logarithm product rule, the Logarithm quotient rule states the following;

$log_b(x/y)=(log_b(x))-(log_b(y))$

One can apply this rule in reverse here to simplify the logarithms on the left side:

$log((x-4)(x-8))-log(5)=0$

$log(\frac{(x-4)(x-8)}{5})=0$

The final step in solving this equation is to use the Logarithm of (1) property. This property states the following:

$log_b(1)=0$

When applying this property here, one can conclude that the evaluator must be equal to (1), therefore, the following statements can be made.

$log(\frac{(x-4)(x-8)}{5})=0$

$\frac{(x-4)(x-8)}{5}=1$

Inverse operations,

$\frac{(x-4)(x-8)}{5}=1$

$(x-4)(x-8)=5$

$(x-4)(x-8)-5=0$

Simplify,

$(x-4)(x-8)-5=0$

$x^2-12x+32-5=0$

$x^2-12x+27=0$

Factor, rewrite the quadratic expression as the product of two linear expressions, such that when the linear expressions are multiplied, the result is the quadratic expression:

$x^2-12x+27=0$

$(x-3)(x-9)=0$

Now use the zero product property to solve. The zero product property states that any number times (0) equals (0).

$x=3,x=9$

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