All categories

1 year ago

A straight line has a gradient of 4 and passes through the point (2,9).

Mathematics

1 answer:

JulijaS [17]1 year ago

8 0

The equation of the given line passes through the point (2,9) y = 4x + 1.

<h3>What exactly is the slope of a line?</h3>

The slope of a line indicates its steepness. The slope is determined mathematically as "increase over run" (change in y divided by change in x).

<h3>A line equation is defined as:</h3>

The conventional form of a line equation is ax + by + c = 0. Here, the coefficients are a and b, the variables are x and y, and the constant term is c. It is a one-degree equation with variables x and y. The coordinates of both the point on the line that appears in the coordinate plane are represented by the values of x and y.

<h3>According to the given data:</h3>

m = 4

equation of the line = y = mx + c

substituting the value of m = 4

y = 4x + c

the point (2,9):

putting the points in the line of the equation:

x = 2

y = 9

So,

y = mx + c

9 = 4 * 2 + c

9 = 8 + c

c = 1

The equation of the given line y = 4x + 1.

To know more about equation of the line visit:

brainly.com/question/2564656

#SPJ9

You might be interested in

Mr. Jones is four times as old as his son. Six years ago he was ten times as old as his son. How old is the son now?

Advocard [28]

Answer:

After 16 years …mr James age =4X+16 and his son's age will be X+16

As per the question in 16 years his age will be 2 twice

(4X+16)=2(X+16)so by simplifying this we will get 2X=16..and X=16/2=8

Step-by-step explanation:

6 0

3 years ago

A flagpole is located at the edge of a sheer y = 70-ft cliff at the bank of a river of width x = 40 ft. See the figure below. An

Gnom [1K]

I would solve this using tangents. Let h be height of flagpole.
Set up 2 right triangles, each with a base of 40.
The larger triangle has height of "h+70"
Smaller triangle has height of 70.

Now write the tangent ratios:
$tan A = \frac{h+70}{40} , tan B = \frac{70}{40}$

Note: A-B = 9
To solve for h we need to use the "Difference Angle" formula for Tangent
$tan (A-B) = \frac{tanA - tanB}{1+tan A tan B}$
Plug in what we know:
$tan(9) = \frac{ \frac{h+70}{40} - \frac{70}{40}}{1+ (\frac{h+70}{40})(\frac{7}{4})}$
$tan (9) = \frac{ \frac{h}{40}}{ \frac{7h +650}{160}} = \frac{4h}{7h+650}$
$h = \frac{650 tan(9)}{4-7 tan(9)}$
$h = 35.6$

7 0

3 years ago

A plumber charges $130 2 hours of work and $235 for 5 hours of workWhat is the of change in dollars per hour

kogti [31]

Answer:

235

Step-by-step explanation:

Figure the rates per hr.

110/3 = 36 2/3

160/5 = 32.

So, the rates are not the same.

Knowing a bit about plumbers, they normally charge a basic fee to just show up, and then they charge per hr.

In cases like these, where we're asked to project to a new data point (in this case an 8-hr job), you should immediately think of a graph. The x-axis would be the hours worked. The y-axis would be the charge for the work (the cost of the job).

We're given two pairs of values:

(3,110) and (5,160).

The next step is to fit a line to them.

y = mx+b is the general equation for a line.

m = the slope = rise/run = change in y / change in x

Call the change in y, dy (for delta y).

Call the change in x, dx (for delta x).

m = dy/dx = 50/2 = 25

The slope is thus 25, which means for each hour, the price goes up by $25. That means the plumber charges $25/hr.

We also know the plumber charges $110 for a 3-hr job. 3*25 = $75. So the base charge would be $110-75 = $35.

y = 25x + 35

Checking this formula at x=3, we know it is 110.

Checking it at x=5, we obtain:

y = 25*5 + 35 = 125 + 35 = 160.

That checks.

Now to figure an 8-hr job, set x=8 and use the equation"

y = 25*8 + 35.

y = 200 + 35.

y = 235.

That means an 8-hr job costs $235.

3 0

3 years ago

Pam started watching a movie at 2:53 P.M. The movie was 1 hour and 52 minutes long. After the movie, Pam rode her bike for 46 mi

Karo-lina-s [1.5K]

The time Pam got home is 5:25 pm.

<h3>How to calculate time </h3>

Remember that 60 minutes is equivalent to 1 hour. When adding minutes together, when the minutes exceeds 60, convert to an hour.

<h3>How to determine the time Pam got home</h3>

In order to determine the time she got home, add the time she used to watch the movie , to the time she used to ride her bike home to the time the movie started.

2:53 + 1:52 + 46 = 5:25 pm

To learn more about addition, please check: brainly.com/question/19628082

7 0

2 years ago

HELPPPP PLSSSSSSSSSSSSSSSSSSSS

forsale [732]

Answer:

.um g o o g l e look it u p I do that.

5 0

3 years ago