Linear Equations (in Slope-Point Form)
(KS3, Year 9)
- 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. finding the slope from a linear equation in slope-point form
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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). finding the y-intercept from a linear equation in slope-point form
Other Forms of Linear Equations
There are other forms of linear equation.-
The general form of a linear equation is:
the general form of a linear equation - The slope-intercept form of a linear equation is: m is the slope and c is the y-intercept. the slope-intercept form of a linear equation
Beware
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.
y + 1 = ...
Remember, that subtracting a negative number is the same as adding the positive number:
y + 1 = y − −1...
−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.
Worksheet
This test is printable and sendable