Question

Which equation represents a line that passes through 4 6) and is parallel to the line whose equation is 3x - 4y= 6

Answer 1

Parallel means their slopes should equal to each other.

Thus we need to find the slope of the given line ,

Let's do it.....

$3x - 4y = 6$

Subtract sides -3x

$- 3x + 3x - 4y = - 3x + 6$

$- 4y = - 3x + 6$

Divided sides by -4

$\frac{ - 4}{ - 4}y = \frac{ - 3}{ - 4}x + \frac{6}{ - 4}$

$y = \frac{3}{4}x - \frac{3}{2}$

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 :

$slope = \frac{3}{4}$

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We have following equation to find the point-slope form of the linear functions.

$y - y(given \: point) = slope \times (x - x(g \: p) \: )$

Now just need to put the slope and the given point in the above equation.

$y - 6 = \frac{3}{4} \times (x - 4)$

Multiply sides by 4

$4(y - 6) = 3(x - 4)$

$4y - 24 = 3x - 12$

Plus sides 24

$4y - 24 + 24 = 3x - 12 + 24$

$4y = 3x + 12$

Subtract sides -3x

$4y - 3x = 3x - 3x + 12$

$4y - 3x = 12$

And we're done....♥️♥️♥️♥️♥️