the slope of the line through the points (3,-4) and (-7,10) is

Question

answers:  7/5,  -7/2,    -7/5,    -5/7

Answer 1

The slope of a line is a fraction, where the numerator describes the vertical movement and the denominator describes the horizontal movement. Right and up are positive and left or down are negative. To find the vertical movement, choose one point as point 1, and the other as point 2. For this example, I'll use (3, -4) as point 1.

We can find the vertical movement by subtracting the y coordinate of point 1 from the y coordinate of point 2. In this case, that would be 10 - (-4), which is 10 + 4 or 14. This will be the numerator of the slope.

We can find the horizontal movement by subtracting the x coordinate of point 1 from the x coordinate of point 2. In this case, that would be -7 - 3, which is -10. This will be the denominator of the slope.

With a 14 in the numerator and -10 in the denominator, our slope fraction is 14/-10, which reduces to 7/-5. The negative sign in the denominator could stay there, or it could be moved to the numerator, like this: -7/5.

Fixed, my apologies.

Answer 2

The easiest way to find the slope of a line given two points is (Y₂ - Y₁) over (X₂ - X₁) expressed as a fraction. In this case, (3, -4) (-7, 10) would be (10- -4) over (-7-3) resulting in 14/-10, which when expressed in simplest form is 7/-5 which as a fraction is equal to -(7/5).

Answer 3

the slope of a line, given two points P₁ and P₂ can be found from using the formula (relationship) for the slope of a line (m)

(3,-4) and (-7,10)

m = Δy/Δx = (y₂ - y₁)/(x₂ - x₁) = (10 - (-4))/((-7) - 3) = 14/(-10) = -7/5

it doesn't matter which point use choose as P1 or P2 as long as you plug them into the formula correctly (and, of course, do the arithmetic correctly ;)  - that's why included the parenthesis, just to keep track of signs)

Answer 4

  7/-5 = -7/5