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

m [ slope ] = 8/3

Step-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.

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 = b

Thus this line has an equation of

y = mx + b

↓ ↓

y = 8/3x – 37/3.

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.

the answers are in the images, i received 100% on this assignment. hope this !