Final answer:
To find the equation of a line parallel to y = -2x + c that passes through a given point, use the slope of -2 from the given equation and find the y-intercept by substituting the given point into y = -2x + b, then solve for b.
Step-by-step explanation:
To find the equation of a line that is parallel to the given line y = -2x + c and passes through a given point, we need to identify the slope of the given line and use it in our new equation. For the given line y = -2x + c, the slope is -2. Remember, parallel lines have identical slopes. If the given point through which the new line passes is (X1, Y1), the equation of the line parallel to the given line is y = -2x + b, where b is the new y-intercept.
To find the y-intercept b, we substitute the coordinates of the given point into the equation to get Y1 = -2X1 + b. Then, solve for b to find the y-intercept of the line that passes through the given point. Once we have b, we can write the final equation of the line.
For example, if our given point is (3, 4), we substitute these values to get 4 = -2(3) + b, which simplifies to 4 = -6 + b. Adding 6 to both sides gives b = 10, so the equation of our line is y = -2x + 10.