What’s parallel to 3x+2y=10 in slope intercept form

Answer 1

Hi there Jazmyn!

You have the standard form of the equation of a line, given as 3x + 2y = 10. From here, we should solve for y, thus rewriting the equation in slope-intercept form.

Standard Form: Ax + By = C

Slope-Intercept Form: y = mx + b (where m is the slope and b is the y-intercept at (0,b) )

Point-Slope Form: y-y1 = m * (x-x1)

3x + 2y = 10

-3x -3x

2y = 10 - 3x

2y = -3x + 10

2 2

y = -3/2 * x + 5

Since we recognize this form, y = mx+b, we can identify the slope and intercept.

m = -3/2 (for every 2 steps to the right taken, you take 3 steps down)

b = 5

A parallel line will have this same slope, and since we know the intercept we can change that into anything we want. Arbitrarily, let's just change b to 1.

y = -3/2 * x + 1

Now, that we know the slope of the original line and we've picked a new intercept (0,1), we can use the new intercept as our point for point-slope form for the new line:

y-y1 = m * (x-x1)

y - 1 = -3/2 * (x - 0)

You should probably keep the 0 to be thorough and display point-slope form. And if you'd like to pick your own point, just make sure it's not actually on the original line, so that you've actually drawn a different line that is parallel. Like, don't pick (2, 2) for (x1, y1).

Another quick trick for finding slope and intercept from standard form is using the following equations. These work because the math is exactly the same as when you switch to slope-intercept form!

m = - A / B

b = C / B

Hope this helps! Please reach out with any further questions.

Answer 2

3x + 2y = 10, subtract 3x from both sides the you get

2y = -3x + 10 divide by 2 you get

y = -3/2 x + 5

slope is m = -3/2

y intercept is ( 0, 5 )