Question

4. (10.03 MC) The equation of line CD is y = −2x − 2. Write an equation of a line parallel to line CD in slope-intercept form that contains point (4, 5). (4 points)

y = −2x + 13

y = negative 1 over 2 x + 7

y = negative 1 over 2 x + 3

− 2x − 3

Answer 1

Answer: y = -2x + 13

Explanation:

Parallel lines have the same slope. y = -2x - 2 has a slope of -2 so the line parallel to that will also have a slope of -2.

We have a point (4, 5) and a slope (-2) so we can use the point-slope formula:

y - y₁ = m(x - x₁) ; where (x₁, y₁) is the point and m is the slope

y - 5 = -2(x - 4)

y - 5 = -2x + 8

y = -2x + 8 + 5

y = -2x + 13

Answer 2

The equation of a line parallel to line CD is y = -2x + 13 ⇒ 1st answer

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