What is the slope of the line through the points (-4, 2) and (-16, -6)?
2/3
−5/2
2/5
3/2

Answer:

The slope is equal to [tex]\frac{2}{3}[/tex] . So the right answer is A.

Step-by-step explanation:

We know that if we are given to points of a function we can find out its slope by using the following formula....

[tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Where m is the slope,  [tex]x_{1}[/tex] and [tex]y_{1}[/tex] are the coordinates of the first point, [tex]x_{2}[/tex] and [tex]y_{2}[/tex] are coordinates of the second point.

Let (-4, 2) be [tex](x_{1} , y_{1})[/tex]

Let (-16, - 6) be [tex](x_{2}, y_{2} )[/tex]

then......

The slope of the line will be [tex]\frac{2}{3}[/tex] i.e. option A is the correct answer.

Slope is or gradient of a line is a number that describes both the direction and the steepness of the line.

Slope [tex](m) =\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

We have,

Points (-4, 2) and (-16, -6)

i.e.

x₁ = -4,  x₂ = -16,

And,

y₁ = 2,   y₂ = -6

Now,

Using the above mentioned formula,

Slope [tex](m) =\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]    

i.e.

Slope [tex](m) =\frac{-6-2}{-16-(-4)}[/tex]

On solving we get,

Slope [tex](m) =\frac{-8}{-12}=\frac{2}{3}[/tex]

So, the slope pf the given points is  [tex]\frac{2}{3}[/tex] .

Hence, we can say that the slope of the line will be [tex]\frac{2}{3}[/tex] i.e. option A is the correct answer.

To know more about Slope click here

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