The equation of the line that is parallel to given line is 12x + 3y = -1
Solution:
Given that, the line that is parallel to y = –4x + 3 and has a y-intercept of -1/3
Given equation of line is:
y = -4x + 3
Let us first find the slope of line
The equation of line in slope intercept form is given as:
y = mx + c ------- eqn 1
Where, "m" is the slope and "c" is the y intercept
On comparing the above slope intercept form with given equation of line, we get m = -4
Thus the slope of line with equation y = -4x + 3 is -4
We have to find the slope of line that is parallel to above line
We know that slopes of parallel lines are equal
Therefore, slope of line passing parallel to given line is -4
Now find the equation of line
[tex]\text{Substitute } m = -4 \text{ and } c = \frac{-1}{3} \text{ in eqn 1 }[/tex]
[tex]y = -4x -\frac{1}{3}\\\\3y = -12x -1\\\\12x + 3y = -1[/tex]
Thus the equation of line is found
