Question

Please help asap calculate the slope of the line through the points (6,-8) and (3,-4).

a. Write the equation of the line

b. Is the point (-3,4) on the line you found in part a?

Answer 1

Explanation:

Mathematically, we can calculate the slope

using the formula below;

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

Where (x1.y1) = (6,-8)

(x2, y2) = (3,-4)

So inputing these values into the formula, we have

m = (-4-(-8))/(3-6)

m = (-4+8)/-3 = 4/-3 = -4/3

Now, we want to write the equation of the line;

y= -4/3x + c

to get the value of c, we simply need to use any of the points. We use any of the two points by substituting the values of x and y at that point.

Let’s use (3,-4)

That would give ;

-4 = -4/3(3) + c

-4 = -4 + c

This means c = 0

Thus the equation of the line is y = -4/3x

Now to find out if the point (-3,4) is on the line

We only need to substitute the values of x and y here and see ;

Thus;

4 = -4/3(-3)

Sine 4 = 4

We can conclude that the point is on the line in question