1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
dlinn [17]
2 years ago
6

Given the point (1, 2) and a slope of 4, write the equation in point slope form.

Mathematics
1 answer:
vitfil [10]2 years ago
5 0

This article is about the math term. For other uses, see Slope (disambiguation).

For the grade (incline or gradient or pitch or slope) of any physical feature, see Grade (slope).

Slope: {\displaystyle m=\left({\frac {\Delta y}{\Delta x}}\right)=\tan(\theta )}{\displaystyle m=\left({\frac {\Delta y}{\Delta x}}\right)=\tan(\theta )}

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.[1] Slope is often denoted by the letter m; there is no clear answer to the question why the letter m is used for slope, but its earliest use in English appears in O'Brien (1844)[2] who wrote the equation of a straight line as "y = mx + b" and it can also be found in Todhunter (1888)[3] who wrote it as "y = mx + c".[4]

Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line. Sometimes the ratio is expressed as a quotient ("rise over run"), giving the same number for every two distinct points on the same line. A line that is decreasing has a negative "rise". The line may be practical - as set by a road surveyor, or in a diagram that models a road or a roof either as a description or as a plan.

The steepness, incline, or grade of a line is measured by the absolute value of the slope. A slope with a greater absolute value indicates a steeper line. The direction of a line is either increasing, decreasing, horizontal or vertical.

A line is increasing if it goes up from left to right. The slope is positive, i.e. {\displaystyle m>0}m>0.

A line is decreasing if it goes down from left to right. The slope is negative, i.e. {\displaystyle m<0}m<0.

If a line is horizontal the slope is zero. This is a constant function.

If a line is vertical the slope is undefined (see below).

The rise of a road between two points is the difference between the altitude of the road at those two points, say y1 and y2, or in other words, the rise is (y2 − y1) = Δy. For relatively short distances, where the earth's curvature may be neglected, the run is the difference in distance from a fixed point measured along a level, horizontal line, or in other words, the run is (x2 − x1) = Δx. Here the slope of the road between the two points is simply described as the ratio of the altitude change to the horizontal distance between any two points on the line.

In mathematical language, the slope m of the line is

{\displaystyle m={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}.}m=\frac{y_2-y_1}{x_2-x_1}.

The concept of slope applies directly to grades or gradients in geography and civil engineering. Through trigonometry, the slope m of a line is related to its angle of incline θ by the tangent function

{\displaystyle m=\tan(\theta )}m = \tan (\theta)

Thus, a 45° rising line has a slope of +1 and a 45° falling line has a slope of −1.

You might be interested in
What was his mistake????
stealth61 [152]
He didn't distribute 1/3 to x and 15 before solving
4 0
2 years ago
If a cubic foot of stone weighs 150 lb and a cubic foot of iron weighs 480 lb, what fraction of the second weight is the first o
iris [78.8K]

Answer:

72,000

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Arrange the steps from start to finish to factor this expression using the grouping method x^2-5x-24 drag the tiles to the corre
rosijanka [135]

Answer:

(x - 8)(x + 3)

Step-by-step explanation:

x² - 5x - 24

Consider the factors of - 24 which sum to give the coefficient of the x- term (- 5)

The factors are - 8 and + 3 , since

- 8 × + 3 = - 24 and - 8 + 3 = - 5

Use these factors to split the x- term

x² - 8x + 3x - 24 ( factor the first/second and third/fourth terms )

= x(x - 8) + 3(x - 8) ← factor out (x - 8) from each term

= (x - 8)(x + 3) ← in factored form

7 0
2 years ago
Plz answer these 2 i really need help I'm not all that smart
kati45 [8]
Answer: 141.7 cm3

Explanation: you multiple 6.1, 6.7, 10.4 then divide by 3 which equals 141.68. Round it and we’re left with 141.7 cm3.
8 0
2 years ago
Read 2 more answers
PLS HELP MEEEEE 1. An Amazon packaging plant can ship 315 packages in 7 hours. What is the constant of
Sati [7]
45 packages are shipped in one hour. I divided 315 by 7
4 0
3 years ago
Read 2 more answers
Other questions:
  • Nestor need 750 centimeters of rope . Rope comes in lengths of 4 1/2 meters and 9 meters at the hardware store. Which length of
    10·1 answer
  • What is the equation for synthetic division
    9·1 answer
  • bicycle, A company that makes dice (cube), is looking to change The size of the days they produce. The current days have edge le
    14·1 answer
  • jill used stones that were each 3)4 of a foot to build a wall. dhe piled 6 stones on top of each fractional wall
    5·2 answers
  • At the local pet store, zebra fish cost $2.10 each and neon tetras cost $1.85 each. If Marsha bought 13 fish
    8·1 answer
  • Multiply.<br> 8u2y6.2u?y?<br> Simplify your answer as much as possible.
    5·1 answer
  • Whoever finishes this gets "brainliest".<br>just for fun<br>35a^7--11a^7
    12·1 answer
  • Tom reports that the ratio of teachers to students at South High School and North High School is the same. There are 45 teachers
    9·1 answer
  • If a bag contains 18 red, 6 yellow, 24 blue, and 8 white balloons, what is the part-lo-whole ratio of white balloons to
    11·2 answers
  • Solve for x in the following problem: 9 = 3/5x
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!