Given:
Line: x + y = 3
Point: (x, y) ==> (-3, 2)
Let's find the equation of the line passing through the given point and parallel to the given line.
Apply the slope-intercept form:
y = mx + b
Where:
m is the slope
b is the y-intercept.
Rewrite the given equation in slope-intercept form:
x + y = 3
Subtract x from both sides:
x - x + y = -x + 3
y = -x + 3
Therefore, the slope of the original line is -1.
Parallel lines have equal slopes.
Hence, the equation of the parallel line is:
m = -1.
Now, plug in -1 for m, then input the coordinates of the point (-3, 2) for the values of x and y respectively.
Thus, we have:
[tex]\begin{gathered} 2=-1(-3)+b \\ \\ 2=3+b \\ \\ b=2-3 \\ \\ b=-1 \end{gathered}[/tex]
The y-intercept of the parallel line is -1.
Therefore, the equation of the parallel line in slope-intercept form is:
[tex]y=-x-1[/tex]
• ANSWER:
[tex]y=-x-1[/tex]
