write the equation for a line that is parallel to the line 2x+3y=6 and passes through the point (0,4)

Answer 1

Parallel lines have the same slope. Your first step is to turn your equation into the slope-intercept form; y = mx + b.

2x + 3y = 6 --> move the 2x to the other side of the equal sign by subtracting the term.

2x - 2x + 3y = -2x + 6

3y = -2x + 6 --> divide both sides by 3

y = -2/3x + 2 --> the slope is -2/3

Now we can use point-slope form; y - y1 = m(x - x1), where x1 and y1 are the coordinates for the point you're given (0,4). Plug in numbers.

y - 4 = -2/3(x - 0) --> factor out

y - 4 = -2/3x --> add 4 to both sides

y = -2/3x + 4 --> same slope and passes through the point (0,4)

Also, since the x-coordinate of the given point was 0, you were really just changing the y-intercept. Notice that's the only change.

Answer 2

Determine the slope, m, of 2x + 3y = 6.

(0, 4) is the y-intercept. Put both in the slope-intercept form

y = mx + 4