Slope Intercept Form

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

y=mx+c

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, y = mx+c, x and y 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 y = mx + c 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.

Also, read:

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 “y=”, hence it is easy to graph it or solve word problems based on it. We just have to put the x-values and the equation is solved for y.

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:

y_2,-y₁=m(x₂-x₁)

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

m=(y_2,-y₁)/(x₂-x₁)

Word Problems

Problem 1: Find the equation of the straight line that has slope m = 3 and passes through the point (–2, –5).

Solution: By the slope-intercept form we know;

y=mx+c

Given,

m=3

As per the given point, we have;

y = -5 and x = -2

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

-5 = 3(-2) + c

-5 = -6+c

c = -5 + 6 = 1

Hence, the required equation will be;

y = 3x+1

Problem 2: Find the equation of the straight line that has slope m = -1 and passes through the point (2, -3).

Solution: By the slope-intercept form we know;

y=mx+c

Given,

m=-1

As per the given point, we have;

y = -3 and x = 2

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

-3 = -1(2) + c

-3 = -2 + c

c = -3+2 = -1

Hence, the required equation will be;

y = -x-1

Practice Problems

1. Find the slope of the line y=5x+2
2. Find the intercept of the line y=-2x+9
3. Find the slope of the line which crosses the line at point (-2,6) and have an intercept of 3