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

Answer:

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

Step-by-step 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

Answer:

y = 3x - 2      slope-intercept

3x - y = 2      standard form

Step-by-step 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

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