Slope Intercept Form: Slope Intercept Form Definition and Graph

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Slope intercept form is the general form of straight-line equation. It is represented as:

Here, c is the y-intercept and m is the slope, hence it is called a slope-intercept form.

Straight line equation gives the graph of a straight line. They are also called linear equations and consist of simple variables. As we can see in the expression, , and are the variables, where x is an independent variable and y is a dependent variable. If we put the values of x, then we can get the respective values of y and then we plot the graph.

Slope Intercept Form Definition

The graph of the linear equation is a line with m as slope, m and c as y-intercept. This form of the linear equation is called slope-intercept form. The values of m and c are real numbers.

The slope, m, represents the steepness of a line. The slope of the line is also termed as gradient, sometimes. The y-intercept, b, of a line, represents the y-coordinate of the point where the graph of the line intersects the y-axis.

Slope Intercept Form Graph

When we plot the graph for slope intercept form equation, we get a straight line. Slope-intercept is the best form. Since, it is in the form hence it is easy to graph it or solve word problems based on it. Substitute the x-values and the equation is solved for.

The best part of slope-intercept form is that we can get the value of slope and the intercept directly from the equation.

Point Slope Intercept Form

The point slope form is also a type of slope intercept form where the distance between the two points is estimated by drawing a straight line between them. Basically, this form is taken from the theory of finding the slope or steepness of a line when two points are given.

The point slope form formula is given by:

Therefore, from the above equation we can derive the slope formula,

Word Problems

Problem 1: Find the equation of the straight line that has slope and passes through the point

Solution: By the slope-intercept form we know;

Given,

As per the given point, we have;

Hence, putting the values in the above equation, we get;

Hence, the required equation will be;

Problem 2: Find the equation of the straight line that has slope and passes through the point

Solution: By the slope-intercept form we know;

Given,

As per the given point, we have;

Hence, putting the values in the above equation, we get;

Hence, the required equation will be;

Example: 3 Find the slope of the line which crosses the line at point and have an intercept of

By the slope-intercept form we know;

Given,

As per the given point, we have;

Hence, putting the values in the above equation, we get;

Hence, the required equation will be,