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## What is the slope of the line that passes through the points (5, 1) and (2, -7)?

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What is the slope of the line that passes through the points (5, 1) and (2, -7)?

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Mathematics
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2021-08-13T20:10:07+00:00
2021-08-13T20:10:07+00:00 2 Answers
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## Answers ( )

Answer:m [ slope ] = 8/3Step-by-step explanation:What is the slope of the line that passes through the points (5, 1) and (2, -7)?

m = ∆y / ∆x

m = y₂ – y₁ / x₂ – x₁

| (5, 1) → (x₁, y₁) | (2, -7) → (x₂, y₂) |

[each coordinate will correspond (directly go to) to the variables shown]

m = (-7) – (1) / (2) – (5)

m = -8 / -3

m = 8 / 3

This means that this line has a rise of 8 and a run of 3.

Up 8 and right 3 proportionally, it would touch the opposite corners of a plane that was 8 by 3 units.

Slope can be thought of as the steepness of a line, the greater the slope, the greater the steepness.

These points are generally known as cartesian coordinates.

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Once you have the slope, you can back track from one of the coordinates to find the equation of the line.

Just multiply the slope by the x of either coordinate, make it opposite, and then add that to the y of that coordinate to get

b[the y-intercept; where it crosses the y axis, x is always 0]Since (2, -7) is closer to the y axis than (5, 1) it is more convenient.

In (2, -7), 2 is the x variable and -7 is the y variable.

-mx + y = (-8/3)(2) + (-7) = -16/3 + (-21/3)

21/3 is the same as 7 [so it will have a common denominator].

-16 + -21 / 3 = -37/3 =

bThus this line has an equation of

y = mx + b

↓ ↓

y = 8/3x – 37/3.

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Or you can refer to point slope which is what is taught:

y – y₁ = m(x – x₁).

You can tell that there are some similarities to this and the slope formula.

m = ( y₂ – y₁ / x₂ – x₁ ) →

m × ( x₂ – x₁ ) =

( y₂ – y₁ / x₂ – x₁ ) × ( x₂ – x₁ )

[multiply the denominator by both sides]

m ( x₂ – x₁ ) = y₂ – y₁

[x₂, and y₂ can just be x and y since you only need the initial coordinate and slope, because the second coordinate can be anything along that line]

m ( x – x₁ ) = y – y₁ →

y – y₁ = m(x – x₁)

[symmetric property of equality]

if a = b, b = a.

-7-1/2-5 because to solve, you do y2-y1/x2-x1

So you get -6/-3, which equals 2

SLOPE IS 2