How are key features of a linear function identified and interpreted from a description?

Consider the graph of the line y = x – 4 and the point (−4, 2).

Hitman42 [59]

Answer:

a. The slope of a line parallel to the given line is 1

b. A point on the line parallel to the given line, passing through (−4, 2), is (1,7)

c. The slope of the line perpendicular to the given line is -1

d. A point on the line perpendicular to the given line, passing through (−4, 2), is (3,-5)

Step-by-step explanation:

The equation of the line in Slope-intercept form is:

$y=mx+b$

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

a. For the line $y = x - 4$

You can identify that:

$m=1$

By definition, two lines are parallel if they have the same slope. Then, the slope of a line parallel to the given line is:

$m=1$

b. The equation of the line in Point-slope form is:

$y -y_1 = m(x - x_1)$

Where m is the slope and ( $x_1,y_1$ ) is a point of the line.

Given the point (-4,2), substitute this point and the slope of the line into the equation:

$y -2 = (x +4)$

Give a value to "x", substitute it into this equation and solve for "y":

For $x=1$ :

$y -2 = (1 +4)$

$y= 5+2$

$y= 7$

Then, you get the point (1,7)

c. The slopes of perpendicular lines are negative reciprocals, then the slope of a line perpendicular to the given line is:

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

d. Given the point (-4,2), substitute this point and the slope of the line into the equation:

$y -2 = -1(x +4)$

$y -2 = -(x +4)$

Give a value to "x", substitute it into this equation and solve for "y":

For $x=3$ :

$y -2 = -(3 +4)$

$y= -7+2$

$y= -5$

Then, you get the point (3,-5)

8 0

3 years ago

Find the GCF for the list. - 6x^2, 21x^3

wolverine [178]

Answer:

3x^2

Step-by-step explanation:

3x^2 can be factored out of each

-6x^2 = 3x^2(-2)

21x^3 = 3x^2(7x)

6 0

3 years ago

A local gym instructor has a course load that allows her to teach eight classes. At an interest meeting, 8 people wanted high-‐

cricket20 [7]

Answer:

The final curse load of the local gym instructor is this:

High-‐impact aerobics = 1

Low-‐impact aerobics = 4

Jazzercise = 1

Step exercise = 2

Step-by-step explanation:

1. Let's apportion the class load using the Hamilton method

Number of classes the local gym instructor can teach = 8

Total number of students that want to take a class = 114 (8 people wanted high-‐impact aerobics, 64 wanted low-‐impact aerobics, 11 wanted jazzercise, and 31 wanted step exercise)

Standard divisor = 114/8 = 14.25

Now, we can apportion the students in in Standard quotas, this way:

High-‐impact aerobics = 8/14.25 = 0.5614

Low-‐impact aerobics = 64/14.25 = 4.49

Jazzercise = 11/14.25 = 0.7719

Step exercise = 31/14.25 = 2.1754

Now, we find the Minimum quota, just considering the whole number and don't taking into account the decimals, this way:

High-‐impact aerobics = 0

Low-‐impact aerobics = 4

Jazzercise = 0

Step exercise = 2

As we can see we have 6 classes and there are 2 still pending. Those 2 goes to the classes with the highest decimal portion, in this case, Jazzercise .7719 and High-‐impact aerobics with .5614.

The final course load is this:

High-‐impact aerobics = 1

Low-‐impact aerobics = 4

Jazzercise = 1

Step exercise = 2

7 0

3 years ago

Darla bought 0.9 kilogram of red grapes and 0.35 kilogram of green grapes.

madam [21]

keep trying good luck to you

3 0

3 years ago

What is the answer.

Alenkasestr [34]

√11 √5 = √(11 * 5) = √55 = approx 7.42 (rounded)

4 0

4 years ago