Question

3x- y = -2. ; (2,4)

Write an equation for the given line that is parallel to the given line and passes through the given point

Answer 1

y=3x-2 or write as 3x-y=2

Explanation:

Write the equation as y=mx+b

y=3x+2

Gradient = 3

for parralel line gradient =3

(y-4)/(x-2) = 3

y-4=3x-6

y=3x-2

Answer 2

y = 3x - 2 slope-intercept

3x - y = 2 standard form

Explanation:

Parallel lines have the same slope.

The slope-intercept form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept

We have the equation of a line in the standard form. Convert to the slope-intercept form:

`3x-y=-2` subtract 3x from both sides

`-y=-3x-2` change the signs

`y=3x+2\to \underline{m=3}`

Therefore the slope-intercept form of the line is:

`y=3x+b`

Put the coordinates of the point (2, 4) to the equation:

`4=3(2)+b`

`4=6+b` subtract 6 from both sides

`-2=b\to b=-2`

Therefore:

`\boxed{y=3x-2}` subtract 3x from both sides

`-3x+y=-2` change the signs

`\boxed{3x-y=2}`