Write the equation of the line that passes through the points (-1,-4) and (9,-5).

Mathematics

1 answer:

Vera_Pavlovna [14]3 years ago

4 0

Answer:

The equation in point-slope form is: $y+4=\frac{-1}{10}(x+1)$

Step-by-step explanation:

Write the equation of the line that passes through the points (-1,-4) and (9,-5).

The point slope form is: $y-y_1=m(x-x_1)$

Where m is slope and x₁ and y₁ are the points given

Finding Slope

Slope can be found of given points using formula: $Slope=\frac{y_2-y_1}{x_2-x_1}$

We have $x_1=-1, y_1=-4, x_2=9, y_2=-5$

Putting values and finding slope

$Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-5-(-4)}{9-(-1)}\\ Slope=\frac{-5+4}{9+1}\\ Slope=\frac{-1}{10}$

So, slope m = -1/10

Using point (-1,-4) and slope m = -1/10 the equation is:

$y-y_1=m(x-x_1)\\y-(-4)=\frac{-1}{10}(x-(-1))\\y+4=\frac{-1}{10}(x+1)$

So, the equation in point-slope form is: $y+4=\frac{-1}{10}(x+1)$

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How the heck do I do this? And what’s the answer?

stira [4]

Answer:

Option A

Step-by-step explanation:

We need to find two expressions that, when simplified, give the same results.

1) First, simplify the expression stated in the question. Multiply each of the terms in the parentheses by the number that is next to them. This would mean you have to multiply both 9x and -6 by $\frac{2}{3}$ . You also have to multiply $\frac{1}{2}x$ and $-\frac{1}{2}$ by 4. Then, simplify.

$\frac{2}{3}(9x-6) + 4 (\frac{1}{2} x - \frac{1}{2})\\\frac{18}{3}x- \frac{12}{3} + \frac{4}{2}x -\frac{4}{2} \\6x - 4 + 2x - 2$

2) Now, combine the like terms.

$6x - 4 + 2x - 2$

$8x - 6$

So, we need to find which of the expressions listed equal 8x - 6.

3) Let's try option A. Do the same as before. Multiply each of the terms in the parentheses by the number that is next to them. So, multiply 4x and -12 by $\frac{3}{4}$ . Also, multiply 30x and 18 by $\frac{1}{6}$ . Then, combine like terms and simplify.