The equation given has a slope of -3. See it? The equation we are looking for must have the same slope because the lines are parallel to each other. This means the lines never meet or touch on the xy-plane.
We use the point-slope formula to find the equation.
Here is the point-slope formula:
y - y_1 = m(x - x_1)
y - 4 = -3(x - (-3))
y - 4 = -3(x + 3)
y - 4 = -3x - 9
We now isolate y to find our equation.
y = -3x - 9 + 5
y = -3x - 4
Done.
Following are the calculation to the given line which is parallel:
Given:
[tex]\bold{ line: \ y=-3x+4}\\\\\bold{ point: (-3,4)}[/tex]
To find:
Calculating the equation=?
Solution:
General equation of a line: [tex]\bold{y = mx + c}[/tex]
Equation of a line: [tex]\bold{y-y_1=m(x-x_1)}[/tex]
By comparing the line equation with the general equation of a line:
[tex]\to \bold{m=-3}\\\\\to \bold{c=4}\\\\[/tex]
Using a line equation and put the point and slope value in it:
[tex]\bold{Point: (-3,4)}\\\\\bold{m=-3}[/tex]
[tex]\to \bold{y-4=-3(x-(-3))}\\\\\to \bold{y-4=-3(x+3)}\\\\\to \bold{y-4=-3x-9}\\\\\to \bold{y=-3x-9+4}\\\\\to \bold{y=-3x-5}\\\\[/tex]
Therefore, the final answer is "[tex]\bold{y=-3x-5}[/tex]"
Learn more:
brainly.com/question/1407546
