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Greeley [361]
3 years ago
9

What is an equation of the line that passes through the points (3, 4) and (-4,-3)?

Mathematics
1 answer:
yan [13]3 years ago
4 0
<h2>Answer:   y =  x  + 1 </h2>

Step-by-step explanation:  

        For us to write the equation for this line, we need to (1) find the slope of the line, and (2) use one of the points to write an equation:

       The question gives us two points, (3, 4) and (-4,-3), from which we can find the slope and later the equation of the line.

<u>Finding the Slope</u>

The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)  

                                         =  (4 - (- 3)) ÷ (3 - (-4))  

                                         =   1  

<u>Finding the Equation</u>

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:

                                 ⇒  y - (-3) =  1 (x - (-4))

                                         y + 3 =  (x + 4)

 

we could also transform this into the slope-intercept form ( y = mx + c)

                                    since  y + 3 =  (x + 4)

                                             ⇒     y = x + 1

                                       

<em>To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.</em>

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4vir4ik [10]

The translation of the given sentence into an equation is: 7(b + 3) = 1.

<h3>How to Translate a Sentence into an Equation?</h3>

Variables can be used to represent an unknown quantity when translating statements into equation. The word "times" is represented as or means "×" (multiplication). "Sum" means addition as well.

Thus, the sentence given can be translated as shown below:

The unknown number is represented as variable b.

"The sum of a number (b) and 3" would be translated as: b + 3.

"Seven (7) times the sum of a number and 3 (b + 3)" would therefore be: 7(b + 3).

Therefore, translating the whole sentence into an equation, we would have:

7(b + 3) = 1.

Thus, the translation of the given sentence into an equation is: 7(b + 3) = 1.

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