Question

what is the equation of the line passing through the point (4,1) that is parallel to the line with the equation 6x - 3y = 21

Answer 1

The correct answer is A hope this helps

Answer 2

When the two lines are parallel then the slope of both the line are equal. The equation of the line passing through the point (4,1) that is parallel to the line with the equation $6x - 3y = 21$ is,

$2x-y=7$

Given Information-

The line passes through the point (4,1).

The equation of the line which is parallel to the line passes through (4,1) is,

$6x - 3y = 21$

Rewrite the equation as,

$-3y=-6x+21$

Divide by -3 both the sides of the equation.

$y=2x-7$

Standard equation of the line-

The standard form of the equation of the line is,

$y=mx+b$

Here m is the slope of the line. Compare it with the given equation of the line we get,

$m=2$

When the two lines are parallel then the slope of both the line are equal.

The equation of the line passes through (4,1) is given as,

$(y-y_1)=m (x-x_1)$

Put the values,

$(y-1)=2 (x-4)$

$y-1=2x-8$

$2x-y=7$

Hence, the equation of the line passing through the point (4,1) that is parallel to the line with the equation $6x - 3y = 21$ is,

$2x-y=7$

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