All categories

3 years ago

Suppose f is a linear function such that f(3 = 5 and f(7 = -4. find the equation for f

1 answer:

7 0

$\displaystyle\\ 
f(3) = 5 \\ 
f(7) = -4\\\\
\texttt{Solve:}\\\\
f(x)=ax+b ~~~\Longleftrightarrow~~~ y=ax+b~~~\Longleftrightarrow~~~ ax+b-y=0\\\\
-------\\
3a+b-5=0~~~(E1)\\ 
7a+b+4=0~~~(E2)\\
---\\
E2 - E1\\
4a+9=0\\
4a =-9\\\\
\boxed{a = -\frac{9}{4} = -2,25}\\\\
3\times \Big(-\frac{9}{4}\Big) + b -5 = 0\\\\
-\frac{27}{4} -5+ b = 0\\\\
\frac{-27-20}{4} + b = 0\\\\
-\frac{47}{4} + b = 0\\\\
\boxed{b = \frac{47}{4} = 11,75}$

You might be interested in

Line AB contains points A(-6,1) and B(1,4).

Free_Kalibri [48]

To solve this problem you must apply the proccedure shown below:

1- You have that the equation of the line is:

$y=mx+b$

Where $m$ is the slope and $b$ is the y-intercept.

2- Based on the information given in the problem, the lines $AB$ and $CD$ are parallel, which means that both have the same slope. Therefore, you can calculate the slope of $AB$ :

$m=\frac{y2-y1}{x2-x1}$

$m=\frac{4-1}{1-(-6)}=\frac{3}{7}$

3- Use the coordinates of the point $D(7,2)$ to calculate the y-intercept:

$2=\frac{3}{7}(7)+b$

4. Solve for $b$ :

$b=2-3=-1$

5. The equation of the line $CD$ is:

$y=\frac{3}{7}x-1$

The answer is: $y=\frac{3}{7}x-1$

6 0

3 years ago

Juan and his father went on a driving trip.

Jet001 [13]

Answer:

162

Step-by-step explanation:

260/2=130

130+32=162

8 0

3 years ago

Read 2 more answers

What is the reason for each step in the solution of the equation?

user100 [1]

Answer in the attachment.

3 0

3 years ago

Consider the formula for the slope between two coordinate points, m, shown below. Which of the following equations is equivalent

o-na [289]

Answer:

Answer is A

Step-by-step explanation:

$m = y2 - y1 \div x2 - x1 \\ y2 = m(x2 - x1) + y1$

6 0

3 years ago

Which description best compares the graphs given by the equations:

nexus9112 [7]

x - 5y = -5, -5x - 25y = 25

First, you'll need to get the x variable by itself.

x - 5y = -5
 +5 +5
 x = 0
So x is plotted on the 0.

For the second part of the first equation, you'll be looking for what the y variable represents.

x - 5y = -5
-x -x
 -5y = -5
 5 5
 y = 1
So y is plotted on the 1 on the vertical line above the 0.

For the first part of the second equation, you'll do the same thing as in the first equation.

-5x - 25y = 25
 +25 +25
 -5x = 50
 5 5
x = 10
So the x for this equation is plotted on 10 on the horizontal line.

For the second part of the second equation, you will do the same thing as in the first equation.

-5x - 25y = 25
+5 +5
 -25y = 30
 25 25
y = 1.2
So the y for the second half of the second question is plotted on 1.2 on the vertical line.

<h2>Answer: B) Perpendicular</h2>

Perpendicular means the lines may or may not be of equal length and they will not be perfectly in line with each other.

Parallel means the lines may or may not be of equal length but will be perfectly in line with each other.

Intersecting means the lines may or may not be of equal length but will touch each other.

6 0

2 years ago