The equation of the line that passes through the given points is y= -4x+23.
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Linear Function</h3>
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:
brainly.com/question/12691830
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