Question

What is an equation of the line that passes through the point left bracket, minus, 3, comma, minus, 6, right bracket(−3,−6) and is parallel to the line 4, x, minus, 3, y, equals, 34x−3y=3?

Answer 1

To find the equation of a line parallel to the given line, we need to find the slope of the given line first.
The given line has the equation 4x - 3y = 3.
To find the slope of this line, we can rewrite it in the slope-intercept form y = mx + b, where m is the slope.
Subtracting 4x from both sides of the equation, we get -3y = -4x + 3.
Dividing all terms by -3, we obtain y = (4/3)x - 1.
We can now see that the slope of the given line is 4/3.

Since the line we are trying to find is parallel to this line, it must also have a slope of 4/3.

Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can substitute the given point (-3, -6) and the slope 4/3 into the equation.

y - (-6) = (4/3)(x - (-3))
y + 6 = (4/3)(x + 3)

To write the equation in standard form, we can multiply through by 3 to eliminate the fraction:

3(y + 6) = 4(x + 3)
3y + 18 = 4x + 12

Rearranging the terms, we have:
4x - 3y = 6

Therefore, the equation of the line parallel to the given line and passing through the point (-3, -6) is 4x - 3y = 6.