The equation represent a line passing through the point (8,9) with a slope of 3 is y= 3x-15.
To make a linear equation, there is several methods depending on what known:
If you know 2 points, for example point A(x1, y1) and B(x2, y2). Then the formula that can be used is:
[tex]\frac{y-y_{1} }{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]
If one point is known, for example point A(x1,y1) and slope m. Then the formula that can be used is:
[tex]y-y_{1}=m(x-x_1)[/tex]
If there are other linear equations that have certain properties (parallel or perpendicular) to the linear equation to be searched for, then we can first find out the slope of the linear equation. If the gradient of another linear equation is m1 and the gradient of the linear equation to look for is m2
If the two lines are parallel
[tex]m_{2}=m_1[/tex]
If the two lines are perpendicular
[tex]m_2=\frac{-1}{m_1}[/tex]
In the problem, it is known 1 point and slope. Then the formula that can be used is:
[tex]y-y_{1}=m(x-x_1)[/tex]
1 known point is (8,9) and the slope of m is 3. Then substitute it into the formula:
[tex]y-9=3(x-8)\\y-9=3x-24\\y=3x-24+9\\y=3x-15[/tex]
Learn more about linear equation here: https://brainly.com/question/13738061
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