# Slope Intercept Form

Linear equation is basically an algebraic equation may either have a constant term or product of constant and a variable. A linear equation may consist of more than one variable. A very important property of an algebraic linear equation is its Slope or gradient. Slope of a linear equation shows that how its angles are farther from the horizontal line of the graph. A linear equation have a form of y = mx + c. There are number of forms of the equation of a line like the intercept form, the general equation of a line, the normalized equation, the Point slope equation, Slope intercept equation etc.

## Slope Intercept Standard Form

The slope intercept form is the equation of a straight line in the form: $y$ = $mx + c$, where, $m$ is the known as the slope of the line with the $x$-axis and $c$ is known as the intercept on $y$-axis.

## How to Find Slope Intercept Form

Let us see how to find slope intercept form from one point OR two point form:
To find the Slope Intercept Form we will use steps shown below,
Step 1: First of all, analyze given line passing through one Point (x$_1$, y$_1$) or line passing through two points (x$_1$, y$_1$) and (x$_2$, y$_2$).
Step 2: Calculate Slope of given line-
If line passes though one point (x$_1$, y$_1$), then slope of line is
m = (y$_1$ / x$_1$),
And If line passes though two points (x$_1$, y$_1$) and (x$_2$, y$_2$), then slope of line is
m = $\frac{y_2 - y_1 }{ x_2 - x_1}$,
Step 3: Calculate slope intercept form by using following formula -
y = mx + c.

## Graph Slope Intercept Form

There are various methods to graph slope intercept of any line. But the easiest way to graph a line is to plot the y intercept first. After that we write slope in fraction form like rise over run for the y intercept just count up or down for the rise over left or right for the run and put next Point. After that we connect both these points and we get our line. To understand that more deeply we take an example of a line which is written in slope intercept form
y = 3x + 2,
Here we can clearly see that the y-intercept of line is 2 and the Slope of a line is m = 3 /1 = 3, now we start Graphing the y intercept by moving up two units on y-axis. After that we further move 3 units UP (rise) and 1 unit RIGHT (run) and put another point. Outcome is the second point. At last we connect both points and finally we get our line.
Let us take an another example of line which is written in slope intercept form,
y = (-3/5) x + 2,
Where 2 is the y intercept and (-3/5) is the slope of a line. So by graphing, we first move 5 points on y- axis. After that from this particular point we move 3 units DOWN (rise) and then we move 5 units to the RIGHT (run). Now the outcome is second point. At last we connect both points. The graph looks like:

## Examples

Example 1: Convert the slope intercepts form y = 4/3 x + 7 into standard form?
Solution: We use following steps to evaluate standard form from slope intercepts form -
Step 1: Given slope intercepts form is y = 4/3 x + 7, here m = 4/3 and c = 7.
Step 2: Now we shift variable at one side and constants on other side, then,
y = 4/3 x + 7,
y - 4/3 x = 7 or 4/3 x - y = -7,
=> 3y - 4x = 21 or 4x - 3y = -21.
So, generated standard form of the given slope intercepts form is 3y -  4x = 21 or 4x - 3y = -21.
Therefore these two steps are useful for converting slope intercepts form to standard form.

Example 2: Find the slope intercepts form of a line which passes through (-1, -6) and slope 6?
Solution: We use following steps for slope intercepts to form a line which passes through (-1, -6),
Step 1: Give, line passes through the point (-1, -6) and slope of the line is 6.
Step 2: Now calculate slope intercepts form by using the following formula-
y = mx + c,
y = (6)x + c …......equation(1),
As we know that it passes through (-1, -6), then -
-6 = 6(-1) + c,
=> c = 0.
Now we put value of ‘c’ in equation (1), then -
y = 6x
So, slope intercepts form of a line, which passes through (-1,-6) is y = 6x
This is a method for evaluation of slope intercepts form of a line which is passes through single point (x$_1$, y$_1$). Similarly we can calculate slope intercepts form for a line which is passes through two points (x$_1$, y$_1$) and (x$_2$, y$_2$).

## Practice Problems

Problem 1:  Find an equation of the line: If y-intercept =  (0, 4) and line passing through the point (5, 3) .
Problem 2: Write the slope intercept form from the graph below: