Answer:
To find the equation of a line parallel to line c, we can use the fact that parallel lines have the same slope.
The equation of line c is given as y = -3/4x - 3, where the coefficient of x (-3/4) represents the slope.
Since line d is parallel to line c, it will have the same slope of -3/4.
Now we have the slope (-3/4) and a point on line d (-2, -2).
Using the point-slope form of a linear equation, we can substitute the values into the formula to find the equation of line d.
The formula is: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Substituting the values into the formula:
y - (-2) = -3/4(x - (-2))
Simplifying, we have:
y + 2 = -3/4(x + 2)
Expanding the brackets:
y + 2 = -3/4x - 6/4
Combining like terms:
y + 2 = -3/4x - 3/2
To make the equation easier to read, we can multiply through by 4 to get rid of the fraction:
4(y + 2) = 4(-3/4x - 3/2)
Simplifying, we have:
4y + 8 = -3x - 6
Rearranging the equation to match the standard form (Ax + By = C), we get:
3x + 4y = -14
Therefore, the equation of line d is 3x + 4y = -14.
Explanation: