Equation of a Line (y = mx + c) An equation of a line in the coordinate plane is in the form of y = mx + c , where: y is the vertical coordinate of...
Equation of a Line (y = mx + c)
An equation of a line in the coordinate plane is in the form of y = mx + c, where:
y is the vertical coordinate of a point on the line.
x is the horizontal coordinate of a point on the line.
m is the slope of the line, which is a measure of how steep the line is.
c is the y-intercept, which is the point where the line crosses the vertical axis.
Slope
The slope of a line is a measure of the steepness or shallowness of the line. If the slope is positive, the line is going up from left to right. If the slope is negative, the line is going down from left to right. If the slope is zero, the line is horizontal.
Y-Intercept
The y-intercept is a point where the line crosses the vertical axis. The y-intercept can be found by setting x to 0 in the equation of the line.
Examples
Line through points (2, 4) and (5, 8) has a slope of 2.
Line passing through points (3, 1) and (6, 5) has a slope of 0.
Line through points (0, 0) and (10, 20) has a slope of 2.
Applications of the Equation of a Line
The equation of a line can be used for various purposes, including:
Finding the equation of a line passing through two points.
Finding the slope of a line.
Finding the y-intercept of a line.
Determining if a line is perpendicular or parallel to another line.