Question

What is the equation of the line that passes through the points (5,3) and (9,-13)?

Answer 1

The equation of the line that passes through the given points is            y= -4x+23.

Linear Function

A line can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=2x+7. Where:

a= the slope

b=constant term that represents the y-intercept.

From the stardard form equation:

• For point (5,3) : 3=5a+b ( equation 1)
• For point (9,-13) : -13=9a+b (equation 2)

Solving the system for equations 1 and 2.

3=5a+b

-13=9a+b * (-1)

3=5a+b

13=-9a-b * (-1)

16= -4a

4= -a

a= -4

If a= -4 from equation 1, you have

3= 5 * (-4)+b

3= -20+b

b=23

Therefore, the line equation is y= -4x+23.

Read more about the system linear equations here:

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