How to find the equation of a line

If we rearrange the second equation it is the same as the first equation. They are the same line.

Since you have y-intercept, this is very easy. You merely need to find the slope. Then you can use the form to find one version of the line.

The slope is:

Thus, for the points and , it is:

Thus, one form of our line is:

If you move the to the left side, you get:

, which is one of your options.

If P1(1, 3) and P2(3, 6), then calculate the slope by m = rise/run = (y2 – y1)/(x2 – x1) = 3/2

Use the slope and one point to calculate the intercept using y = mx + b

Then convert the slope-intercept form into standard form.

The slope intercept form states that . In order to convert the equation to the slope intercept form, isolate on the left side:

The answer is .

A line can only be represented in the form or , for appropriate constants , , and . A graph must have an equation that can be put into one of these forms to be a line.

represents a parabola, not a line. Lines will never contain an term.

To solve this question, you could use two points such as (1.2,0) and (0,-4) to calculate the slope which is 10/3 and then read the y-intercept off the graph, which is -4.

If you have two points, you can always use the point-slope form of a line to find your equation. Recall that this is:

You first need to find the slope, though. Recall that this is:

For the points and , it is:

Thus, you can write the equation using either point:

Now, notice that one of the options is:

This is merely a multiple of the equation we found, so it is fine!

The equation of a line is

y=mx + b where m is the slope

Rearrange the equation to match this:

7x + 28y = 84

28y = -7x + 84

y = -(7/28)x + 84/28

y = -(1/4)x + 3

m = -1/4

P1 (0, 6) and P2 (4, 0)

First, calculate the slope: m = rise ÷ run = (y2 – y1)/(x2 – x1), so m = –3/2

Second, plug the slope and one point into the slope-intercept formula:

y = mx + b, so 0 = –3/2(4) + b and b = 6

Thus, y = –3/2x + 6

First solve for the slope of the line, m using y=mx+b

m = (y2 – y1) / (x2 – x1)

= (15 – 14) / (_–_5 _–_3)

= (1 )/( _–_8)

=_–_1/8

y = –(1/8)x + b

Now, choose one of the coordinates and solve for b:

14 = –(1/8)3 + b

14 = _–_3/8 + b

b = 14 + (3/8)

b = 14.375

y = –(1/8)x + 14.375