Question

What is the slope of the line that passes through the points (1, 3) and (5, –2)?

Answer 1

Slope for a straight line:
\[m=\frac{y_2-y_1}{x_2-x_1}\]
Can you input the values and solve?

Answer 2

wait hold on

Answer 3

4/5?

Answer 4

@LanguageEnthusiast

Answer 5

Um... Close...
\[m=\frac{3-(-2)}{1-5} \Rightarrow m=\frac{3+2}{1-5} \Rightarrow m = \frac{5}{-4}\]

Answer 6

\[m=\frac{-2-3}{5-1} \Rightarrow m=\frac{-2-3}{5-1} \Rightarrow m = \frac{-5}{4}\]
Is the other way to do it, but either ways, in the slope concept:
It doesn't matter which side you start on, it you graphed \(\dfrac{-5}{4}\) or \(\dfrac{5}{-4}\) you would still have the same line.

Answer 7

What is the slope of the line that passes through the points (3, –1) and (–2, –5)?

Answer 8

i need help with one more

Answer 9

Use the formula I told you about:
\[m=\frac{y_2-y_1}{x_2-x_1}\]
Input the values that you are given:
\[(3, –1) ~(–2, –5)\Rightarrow (x_2,y_2)~(x_1, y_1)\]

Answer 10

4/5?

Answer 11

@LanguageEnthusiast

Answer 12

\[m=\frac{-1-(-5)}{3-(-2)} \Rightarrow m=\frac{-1+5}{3+2} \Rightarrow m=\frac{4}{5} \]
So you are correct! :-).

Answer 13

The sum of three consecutive integers is –27. What are the numbers?

Answer 14

@LanguageEnthusiast

Answer 15

Consecutive integers are integers that come one right after the other in the counting order. For example, 3 and 4 are two consecutive integers. 7, 8, and 9 are three consecutive integers.

You are looking for three consecutive integers. Since they are unknowns, we need to use variables. We could call them x, y, and z, but that would not help much because we'd have one equation, x + y + z = -27, with three unknowns which wouldn't give us the three numbers.

The way to solve this problem is to notice the relationship between the three unknown numbers. Since they are consecutive integers, let the smallest one be called x. The next larger one is 1 more than x, so it's x + 1. The third number is one more than the second one so it's (x + 1) + 1, or simply x + 2.

Now we can write the equation using only the variable x. The sum of the three integers is -27, so we write:

(x) + (x + 1) + (x + 2) = -27

We can get rid of parentheses and simplify the left side.

x + x + 1 + x + 2 = -27

x + x + x + 1 + 2 = -27

3x + 3 = -27

Now solve the equation for x to find the smallest of the three numbers.
Then add 1 to it to find the middle number.
Then add 2 to x to find the largest of the three numbers.

Answer 16

@mathstudent55
That is a really good explanation! Kudos to you :-).

Answer 17

@LanguageEnthusiast
Thanks.