Question

What is the slope of the line passing through the following points: `(-3/4 , 2/3) , (1/3, 2/5 )`?

Answer 1

`m=-16/65~~-0.2462`

Explanation:

The slope of a line passing through two points is given by the following slope formula:

`m=(y_2-y_1)/(x_2-x_1)`

We can plug in the values of the two points we have been given where

`(x_1,y_1)=(-3/4,2/3)`

and

`(x_2, y_2)=(1/3, 2/5)`

The numerator of the slope formula is

`y_2-y_1=2/5-2/3=2/5(xx3)/(xx3)-2/3(xx5)/(xx5)=6/15-10/15=-4/15`

The denominator of the slope formula is

`x_2-x_1=1/3-(-3/4)=1/3+3/4=1/3(xx4)/(xx4)+3/4(xx3)/(xx3)`

`=4/12+9/12=13/12`

Finally, the slope formula is

`m=(y_2-y_1)/(x_2-x_1)=(-4/15)/(13/12)=-4/15 * 12/13=-48/195=-16/65`