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:
y2,-y1=m(x2-x1)
Therefore, from the above equation we can derive the slope formula;
m=(y2,-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
- Find the slope of the line y=5x+2
- Find the intercept of the line y=-2x+9
- Find the slope of the line which crosses the line at point (-2,6) and have an intercept of 3