What Is a Linear Equation (in Slope-Point Form)? (Mathematics Lesson)
What Is a Linear Equation (in Slope-Point Form)?
A linear equation is an equation that represents a line.
A linear equation can be written in the form:
On a graph, a linear equation looks like a line:
y and x are the Cartesian coordinates of points on the line.
m is the slope of the line. It tells you the steepness of the line.
(x1, y1) is a point on the line.
A Real Example of a Linear Equation in Slope-Point Form
An example of a linear equation in slope-point form is given below:
If we compare this equation to y − y1 = m(x − x1), we can find the slope and a point on the line.
The number in front of the brackets is the slope.y − 2 = 2(x − 1)
The slope is 2.
A point on the line can be found from the numbers being subtracted from y and x.y − 2 = 2(x − 1)
1 is being subtracted from x. 1 is the x-coordinate of the point.
2 is being subtracted from y. 2 is the y-coordinate of the point.
The point on the line is (1, 2).
Other Forms of Linear Equations
There are other forms of linear equation.
The general form of a linear equation is:
The slope-intercept form of a linear equation is:
m is the slope and c is the y-intercept.
When Points Have Negative Coordinates
In this lesson, we have said that:
the number that is subtracted from the y gives the y-coordinate of a point.
the number that is subtracted from the x gives the x-coordinate of a point.
What if a number is added to the y or x?
Remember, that subtracting a negative number is the same as adding the positive number:
−1 is being subtracted from y, so the y-coordinate is −1.
When a number is added to y or x, the coordinate is negative.