Question

Write the equation of a line that goes through the point ( 2, - 2 ) and is parallel to the line y = 2x - 11.

Answer 1

Answer: y = 2x - 6

Explanation:

Our task is to write a line's equation, given that the line:

• Is parallel to y = 2x - 11
• Passes through the point (2,-2)

Main Idea

Two parallel lines have equal slopes. If line A is parallel to line B, and line A has a slope of m, then the slope of B also has a slope of m.

The slope of y = 2x - 11 is 2; the slope of the line that's parallel to it also has a slope of 2.

Now, we have:

• the line's slope
• a point it passes through

We write the equation in point-slope form:

`\bullet\qquad\sf{y-y_1=m(x-x_1)}`

Substitute the values into this formula:

`\bullet\qquad\sf{y-(-2)=2(x-2)}`

`\bullet\qquad\sf{y+2=2(x-2)}`

`\bullet\qquad\sf{y+2=2x-4}`

`\bullet\qquad\sf{y=2x-4-2}`

`\bullet\qquad\sf{y=2x-6}`

Therefore, the line's equation is y = 2x - 6.

Answer 2

y = 2x - 6

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given the line

y = 2x - 11 ← in slope- intercept form

with slope m = 2

• Parallel lines have equal slopes , then

y = 2x + c ← is the partial equation

to find c substitute (2, - 2 ) into the partial equation

- 2 = 2(2) + c = 4 + c ( subtract 4 from both sides )

- 6 = c

y = 2x - 6 ← equation of parallel line