how do you convert standard form to point slope form?

Question

how do you convert standard form to point slope form?

Answer 1

If you just need to find the slope and y-intercept, there's no need to convert.

Ax + By = C.

The slope = -A/B

The y-intercept = C/B

For example: 3x -2y = 6.

Slope = -3/-2 = 3/2

y - intercept = 6/-2 = -3

Answer 2

Since there are infinitely many points on the graph of a linear equation there are infinitely many point-slope forms for the equation. You need to determine the slope of the line and any point on that line.

Let's say you have the equation:

5x - 4y = 12.

One way to find the slope is to solve for y and determine the coefficient of x:

4y = 5x - 12

y = 5x/4 - 3

That means the slope is 5/4.

To determine some point on the line let x = any number and determine the corresponding y-value.

Let x = 4.

Then y = (5/4)4 - 3 = 2

To write the equation of a line with slope 5/4 and passing through (4, 2) in point-slope form:

(y - 2) = (5/4)(x - 4)

Here is a Desmos graph illustrating the above.

Use the slider on point P and take a look at row 8.

desmos.com/calculator/da8wfqsdx3