# Converting Slope Intercept to Standard Form

Standard form of equation is of the form: ax + by + c = 0 and slope intercept looks like y = mx + c, where m is the slope of a line and c is the y-intercept. If one is clear about basics can easily convert slope intercept form to the standard form.
In mathematics, if we want to find the slope then it is necessary that you have two axis co-ordinates points. For example if we have co-ordinates $(x_1,y_1)$ and second co-ordinates $(x_2,y_2)$ then Slope ‘m’ is
m = $\frac{y_2-y_1}{x_2-x_1}$
And an equation of a line which pass through a co-ordinate $(x_1,y_1)$ is,
y - y$_1$ = m (x - x$_1$).

How to Convert Slope Intercept to Standard Form
We can convert slope intercept form y = mx + b into standard form Ax + By + C = 0 using some basic arithmetic operations.
y = mx + c
Subtract mx from both the sides
y - mx = mx + c - mx
y - mx = c
Subtract c from both the sides,
y - mx - c = c - c
y - mx - c = 0
Rearrange the above equation
-mx + y - c = 0
Let m be equatl to a/b
-a/b x + y - c = 0
Multiply both sides by b, to get rid of the fraction.
b(-a/b x + y - c = 0)
-a x + by - bc = 0
-ax + by - C = 0 (say bc = C (constant term))
Which is standard from of a equation.

## Examples

Example 1: Find the equation of a line passing through (1, 3) and slope 2.
Solution: The general equation for standard form: y = mx + c
y - 3 = 2 (x - 1)
y - 3 = 2x - 2
y = 2x + 1
This is a Slope Intercept Form of a line.

As we know that if we have a slope ‘m’ and constant ‘b’ of any line than according to slope intercept method,
y = mx + b,

Example 2: Find the equation of line passing through the point (3, -2) and slope 5. Write into the standard form.
Solution:
The equation of the line which passes through point (x_1, y_1) and have slope ‘m’ is
y - y_1 = m (x - x_1),
After finding the slope we find the equation of line which passes through the co-ordinate (3, -2).
Now we put the values of slope and line on the above formula so the line is
y - (-2) = 5 (x - 3),
y + 2 = 5x - 15
Simplify it
y = 5x - 17 (Which is the slope intercept form)

Now we will be converting slope intercept to standard form.
Now move the ‘x’ term to left hand side.
y - 5x = -17 (standard from of a line)
Which is similar to standard form,
Ax + By = C,
Where A, B and C are integers terms.

## Practice Problems

Practice Problem 1: Write the equation in the standard form which is passing through the point (-4, 5) and slope 10.
Practice Problem 2: Find the equation of line passing through the points (2, 3) and (5,4).
Practice Problem 3 : Write y = -1/2 x + 10 in standard form.