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A line is drawn through (-7, 11) and (8,-9). The equation

y-11 = -4/3(x + 7) is written to represent the line. Which
equations also represent the line? Check all that apply.

User Hamidfzm
by
8.3k points

1 Answer

5 votes

Answer:


\textsf{Slope-intercept form}: \quad y=-(4)/(3)x+(5)/(3)


\textsf{Standard form}: \quad 4x+3y=5

Explanation:

Given linear equation:


y-11=-(4)/(3)(x+7)

The given linear equation is point-slope form.


\boxed{\begin{minipage}{3.7cm}\underline{Slope-intercept form}\\\\$y=mx+b$\\\\where $m$ is the slope\\ and $b$ is the $y$-intercept.\\\end{minipage}}

To write the equation in slope-intercept form, isolate y:


\implies y-11=-(4)/(3)(x+7)


\implies y-11=-(4)/(3)x-(28)/(3)


\implies y-11+11=-(4)/(3)x-(28)/(3)+11


\implies y=-(4)/(3)x+(5)/(3)


\boxed{\begin{minipage}{5.4 cm}\underline{Standard form}\\\\$Ax+By=C$\\\\where $A, B$ and $C$ are constants and $A$ must be positive.\\\end{minipage}}

To write the equation in standard form, eliminate the fraction, bring the terms in x and y to the left of the equation, and the constants to the right:


\implies y-11=-(4)/(3)(x+7)


\implies (y-11) \cdot 3=-(4)/(3)(x+7) \cdot 3


\implies 3y-33=-4(x+7)


\implies 3y-33=-4x-28


\implies 3y-33+4x=-4x-28+4x


\implies 3y-33+4x=-28


\implies 3y-33+4x+33=-28+33


\implies 4x+3y=5

User Codii
by
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