Question

Find the equation of a line which is parallel to the line with the equation 2x + y = 4 and

which passes through the origin.

Answer 1

y = -2x

Explanation:

Given

• 2x + y = 4
• Passes through the origin (0, 0)

Solving

Rewriting the equation

• 2x + y = 4
• y = -2x + 4

New equation

• The slope of the new line is the same (-2) because it is parallel
• The y-intercept is (0, 0)

⇒ y = mx + b [m = slope, b = y-intercept]

⇒ y = -2x + 0

⇒ y = -2x

Answer 2

2x+y=0

Explanation:

Given:

`\displaystyle \large{2x+y=4}\\\displaystyle \large{y=-2x+4}`

To find:

• The equation of line that’s parallel and passes through origin point.

Parallel Definition:

• Both lines have same slope.

Slope-Intercept:

`\displaystyle \large{y=mx+b}`

• m = slope
• b = y-intercept

Therefore, another line is:

`\displaystyle \large{y=-2x+b}`

Since the line passes through origin point which is (0,0). Substitute x = 0 and y = 0 in the equation:

`\displaystyle \large{0=-2(0)+b}\\\displaystyle \large{b=0}`

Therefore, the equation is:

`\displaystyle \large{y=-2x}`

Convert back to standards form:

`\displaystyle \large{2x+y=0}`

Therefore, another line that is parallel to
`\displaystyle \large{2x+y=4}` is 2x+y=0