What is the slope of the line passing through the following points: # (5, -2) ; (2,-6)#?

Question

Nathan Axel · Accepted Answer

The slope is #+4/3#

As (5,-2) is listed first then it is assumed to be the first point.

Given:

For first point the strait line graph #(x_1,y_1)->(5,-2)#

For the second point on the strait line graph #(x_2,y_2)->(2-6)# '~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let m be the slope (gradient)

#m=("change in y")/("change in x")#

Thus we have:#" " m-> (y_2-y_1)/(x_2-x_1) ->((-6)-(-2))/(2-5)#

#=> m=(-4)/(-3) #

But a negative divided by another negative gives a positive answer.

#=> m= 4/3#

The slope is #+4/3#

Genesis Allen · Answer

undefined To find the slope of the line passing through the points (5, -2) and (2, -6), you can use the slope formula:

$$ \text{Slope} = \frac{y_2 - y_1}{x_2 - x_1} $$

Substitute the coordinates of the points into the formula:

$$ \text{Slope} = \frac{(-6) - (-2)}{2 - 5} $$

$$ \text{Slope} = \frac{-6 + 2}{2 - 5} $$

$$ \text{Slope} = \frac{-4}{-3} $$

$$ \text{Slope} = \frac{4}{3} $$

So, the slope of the line passing through the points (5, -2) and (2, -6) is $ \frac{4}{3} $.