How do i find the slope of the line passing through points A (5,4) and B(0,3)?

Question

I LOVE ALGEBRA BUT I HATE GRAPHS I JUST DONT KNOW HOW TO SOLVE THIS PROBLEM, DO I USE Y=MX+B? BUT HOW DO I KNOW WHAT M AND B IS? LIKE HOW DO I SOLVE IT TO GET THOSE?

Oh isee thank you!!!!

Answer 1

If A(x₁, y₁) and B(x₂, y₂) are the coordinates of two points on a straight line, then m, the gradient of AB is DEFINED by:

m = (y₂ - y₁)/(x₂ - x₁) provided x₂ ≠ x₁

In other word, gradient is "the difference in the y-coordinates divided by the corresponding difference in the x-coordinates" . . . . . **

The order of the points is unimportant, as long as we use the same order for top and bottom of our fraction.

So, for your points A(5, 4) and B(0, 3);

gradient of AB = m = (4 - 3)/(5 - 0) = 1/5

{Notice that if we'd done it the other way round m = (3 - 4)/(0 - 5) = -1/-5 = 1/5
and we get exactly the same answer.}

Learn the formula - remember it as a sentence as in ** above - it is a VERY useful formula!

Answer 2

Ans. Slope (m) = 1/5

Slope (m) = (y1 - y2)/(x1 - x2) - (4 - 3)/(5 - 0) = 1/5

Alternatively, substitute both the points in y = mx + b
We have,
4 = m*5 + b... Eqn 1 from point A
3 = m*0 + b... Eqn 2 from point B
We get b = 3 from Eqn 2. Substituting in Eqn 1, we get m = 1/5.

Answer 3

m = (4 - 3) / (5 - 0) = 1 / 5
Line passes thro` (0,3) (so b = 3 and a = 0)
y - b = m.(x - a)
y - 3 = (1/5).(x - 0)
y = (1/5).x + 3

Answer 4

slope=rise/run
slope's equation is (Y2-Y1)/(X2-X1)=(3-4)/(0-5)=-1/-5 the 2 negatives will be cancelled. 1/5

Answer 5

use (y -y1)/(x-x1) = m
(4-3)/(5-0) = m
1/5 = m

Answer 6

slope = (Y2-Y1)/(X2-X1) = (3 - 4)/(0 - 5) = -1/-5 = 1/5