Parallel means their slopes should equal to each other.
Thus we need to find the slope of the given line ,
Let's do it.....
[tex]3x - 4y = 6[/tex]
Subtract sides -3x
[tex] - 3x + 3x - 4y = - 3x + 6[/tex]
[tex] - 4y = - 3x + 6[/tex]
Divided sides by -4
[tex] \frac{ - 4}{ - 4}y = \frac{ - 3}{ - 4}x + \frac{6}{ - 4} \\ [/tex]
[tex]y = \frac{3}{4}x - \frac{3}{2} \\ [/tex]
This is the slope-intercept of the line.
We know that the coefficient of the x in slope-intercept form , is the slope of the line.
Thus the slope of the equation which we want is :
[tex]slope = \frac{3}{4} \\ [/tex]
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We have following equation to find the point-slope form of the linear functions.
[tex]y - y(given \: point) = slope \times (x - x(g \: p) \: ) \\ [/tex]
Now just need to put the slope and the given point in the above equation.
[tex]y - 6 = \frac{3}{4} \times (x - 4) \\ [/tex]
Multiply sides by 4
[tex]4(y - 6) = 3(x - 4)[/tex]
[tex]4y - 24 = 3x - 12[/tex]
Plus sides 24
[tex]4y - 24 + 24 = 3x - 12 + 24[/tex]
[tex]4y = 3x + 12[/tex]
Subtract sides -3x
[tex]4y - 3x = 3x - 3x + 12[/tex]
[tex]4y - 3x = 12[/tex]
And we're done....♥️♥️♥️♥️♥️
