Answer:
The equation of a line parallel to line CD is y = -2x + 13 ⇒ 1st answer
Step-by-step explanation:
* Lets revise the conditions of the parallel lines
- The slopes of the parallel lines are equal
- The form of slope-intercept equation is y = m x + c, where
m is the slope of the line and c is the y-intercept
- The y-intercept means that the line intersect the y-axis at point (0 , c)
- To find an equation of a line parallel to another line, do these steps
# Find the slope of the given line and use it as a slope of the new line
# Substitute x and y in the equation by a point on the new line to find c
* Lets solve the problem
∵ The equation of line CD is y = -2x - 2
∵ The equation of any line is y = m x + c, where m is the slope of
the line
∴ The slope of the line is -2
- The equation of the line parallel to CD will have the same slope
∵ The parallel line have same slopes
∴ The slope of the new line is -2
∴ The equation of the parallel line is y = -2x + c
- To find c use a point on the new line and replace x and y in the
equation by its coordinates
∵ The parallel line contains point (4 , 5)
- Put y = 5 and x = 4 in the equation
∴ 5 = -2(4) + c ⇒ simplify
∴ 5 = -8 + c ⇒ add 8 to both sides
∴ 13 = c
- Write the equation with the value of c
∴ y = -2x + 13
* The equation of a line parallel to line CD is y = -2x + 13
