equation in ax+by=c

Question

What is the equation, in slope-intercept form, of the line parallel to y=7x+3 that passes through the point with coordinates (-3, 3)?

Answer 1

The formula for a line in slope-intercept form is:

y = mx + b

In this equation:

1. m represents the slope of the line.
2. b denotes the y-intercept.

Since parallel lines have identical slopes, the slope of the line you need is the same as that of the given line, which is 7 (as seen in (y = 7x + 3)).

Next, you must determine the y-intercept b for the new line that intersects at the point (-3, 3). You can use the point-slope formula of the equation:

y = mx + b

Now, replace the values with (x = -3), (y = 3), and (m = 7) we get

3 = 7(-3) + b

Now simplify:

3 = -21 + b

To find (b), rearrange the equation:

b = 3 + 21 = 24

Therefore, the equation of the line that runs parallel to (y = 7x + 3) and passes through the point (-3, 3) is:

y = 7x + 24

Answer 2

Hi Kaley

y = 7x + 24

To convert to the form ax + by = c; subtract 7x from both sides to give

-7x + y = 24

Also it is common practice in standard form that the coefficients of x and y are integers and that a is positive so we should multiply the above by negative 1

7x - y = -24

keep in mind that your original line in the form ax + by = c means you again subtract 7x from both sides so,

y = 7x + 3 converted to the form ax + by = c is

-7x + y = 3 and meeting common practice as described above the coefficients

7x - y = -3

Since the lines are parallel they have exactly the same slope, 7.

In Slope Intercept Form you start with the slope and use the coordinates given (-3, 3) to calculate b and complete your equation

Start with the correct form

y = mx + b

We know the slope because the line is parallel to y = 7x + 3

y = 7x + b

We can calculate b by using the coordinates of the point given

3 = 7(-3) + b

3 = -21 + b

” 3 + 21 = b”

3 + 21 = 24 = b

So your line is

y = 7x + 24

You can graph both lines at desmos.com to see that they are parallel,

Hope this helps.