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julsineya [31]
3 years ago
8

Equation of the line (-6,5) and (8,14) in standard form

Mathematics
1 answer:
blsea [12.9K]3 years ago
4 0

Answer:

\huge\boxed{9x-14y=-70}

Step-by-step explanation:

The point-slope form of an equation of a line:

y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}

We have two points (-6, 5) and (8, 14).

Substitute:

m=\dfrac{14-5}{8-(-6)}=\dfrac{9}{14}\\\\y-5=\dfrac{9}{14}(x-(-6))\\\\y-5=\dfrac{9}{14}(x+6)

Thew standard form of an equation of a line:

Ax+By=C

transform:

y-5=\dfrac{9}{14}(x+6)\qquad|\text{multiply both sides by 14}\\\\14y-14\cdot5=14\!\!\!\!\!\diagup^1\cdot\dfrac{9}{14\!\!\!\!\!\diagup_1}(x+6)\\\\14y-70=9(x+6)\\\\14y-70=9x+54\qquad|\text{subtract}\ 9x\ \text{from both sides}\\\\-9x+14y-70=54\qquad|\text{add 70 to both sides}\\\\-9x+14y=70\qquad|\text{change the signs}\\\\9x-14y=-70

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