Write an equation in slope-intercept form for the line that passes through (0, -2) and is parallel to the line whose equation is 3x + 5y = 3.

Answer 1

3x+5y = 3, solve for y

5y= -3x + 3

y= (-3/5)x + 3/5 where -3/5 = the slope of any parallel line

y=(-3/5)x + b where b = the y intercept. to calculate b plug in the point (0,-2)

-2 = (-3/5)(0) + b

b =-2

y=(-3/5)x -2 is the parallel line through the given point

or

3x+5y = -10

Answer 2

Hi Kaira,

Because we want our new line/equation to be parallel to the other line, we know that they must have the same slope.

3x + 5y = 3

5y = -3x + 3

y = (-3/5)x + 3

Therefore, our new line will have a slope of -3/5.

Now let us plug in the x and y value of our coordinate, (0,-2), that we want our new line to pass through.

-2 = (-3/5)(0) + b

-2 = 0 + b

b = -2

Therefore, the equation of our new line will be y = (-3/5)x - 2

Answer 3

Parallel lines have the same slope, so the first thing you will want to do is determine the slope of the line 3x + 5y = 3. There are several ways to do this; you can rewrite the equation in slope-intercept form, you can find two points which satisfy the equation and use them to find the slope, or you can graph it and determine the slope that way.

Once you know the slope of 3x + 5y = 3, the line that is parallel must have the same slope and go through the point (0, -2). So you'll want to write the equation in point-slope form; y - y₁ = m(x - x₁).

Once you have the equation in point-slope form, you would rewrite the equation in slope-intercept form by solving the equation for y (i.e y = mx + b).