Answered

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What is the equation of the line parallel to 3x + 5y = 11 that passes through the point (15, 4)?3x-29= 3x - 295y-y-x-21y--x+533y=-5* +13Mart this and returnSavond uit

What Is The Equation Of The Line Parallel To 3x 5y 11 That Passes Through The Point 15 43x29 3x 295yyx21yx533y5 13Mart This And ReturnSavond Uit class=

Sagot :

Recall that two equations in standard form represent parallel lines if they are as follows:

[tex]\begin{gathered} Ax+By=C_1, \\ Ax+By=C_2, \end{gathered}[/tex]

Where A>0, and all the coefficients are integers.

Therefore the equation of a parallel line to the given line is as follows:

[tex]3x+5y=k[/tex]

Since the parallel line passes through (15,4) then:

[tex]3*15+5*4=k.[/tex]

Simplifying the above result we get:

[tex]\begin{gathered} 45+20=k, \\ k=65. \end{gathered}[/tex]

Therefore:

[tex]3x+5y=65.[/tex]

Solving the above equation for y we get:

[tex]\begin{gathered} 3x+5y-3x=65-3x, \\ 5y=-3x+65, \\ \frac{5y}{5}=-\frac{3x}{5}+\frac{65}{5}, \\ y=-\frac{3}{5}x+13. \end{gathered}[/tex]

Answer: Last option.

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