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german
2 years ago
11

Which is an equation of the line that passes through the points (5, 2) and (10, -3)?

Mathematics
1 answer:
sashaice [31]2 years ago
4 0

Answer:

y = -x + 7

Step-by-step explanation:

Hi there!

We are given the following points:
(5,2) and (10,-3)

We want to find the equation of the line that passes through these 2 points

There are 3 ways to write the equation of the line, yet the most common way is slope-intercept form, which is y=mx+b (m is the slope and b is the y intercept).

First, let's find the slope of the line.

The slope can be calculated from 2 points using the equation \frac{y_2-y_1}{x_2-x_1}, where (x_1, y_1) and (x_2, y_2) are points

We have everything we need to find the slope, but let's label the values of the points to avoid confusion and mistakes.

x_1=5\\y_1=2\\x_2=10\\y_2=-3

Now substitute these values into the formula to find the slope

m=\frac{y_2-y_1}{x_2-x_1}

m=\frac{-3-2}{10-5}

Simplify

m=\frac{-5}{5}

Divide

m=-1

The slope of the line is -1

We can substitute this value as m in y=mx+b.

Here's the equation of our line so far:

y=-x+b

Now we need to find b

As the equation passes through the points (5,2) and (10,-3), we can use either point to find the value of b

Taking (5,2) for example:

Substitute 5 as x and 2 as y

2=-5+b

Add 5 to both sides

7=b

Substitute 7 as b in the equation

y = -x + 7

Hope this helps!

See more on this topic here: brainly.com/question/27166723

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