Overview: Graphing Linear Equations
One way to represent a linear equation is to graph it on the coordinate plane. In order to graph the line accurately, it is important to know what the slope of the line is. If the equation is in the form y = mx +b the point at which the line crosses the y axis of the graph is called the y intercept.
Definition of the Slope of the Line
The slope of the line is how steep the line is. It can be measured by the ratio of the vertical change between any two points on a line divided by the horizontal change between any two points on the same line. The horizontal change cannot be equal to zero, because dividing by zero is undefined. If you know the y coordinates of any two points, you know the vertical change, because the y axis on a graph is vertical. If you know the x coordinates of any two points, you know the horizontal change, because the x axis is horizontal.
Finding the Slope of a Line
For any points along a line, the slope is a constant, usually represented by the letter m. The way to find the slope of the line is to use the coordinates, subtract, and divide to get the ratio. For example, one point on the line has the coordinates (1, 3) and another has the coordinates (6,7). What is the slope? The vertical change is 7-3 or 4 divided by the horizontal change 6-1 or 5, or 4/5.
Positive Slope and Negative Slope
In the example of the line with slope 4/5, the slope is positive, and it rises from left to right. Suppose one point on the line is (-4, 3) and another point is (1, -3). Then the vertical change will equal -3-3 or -6 divided by the horizontal change. The horizontal change of (1-(-4) will change its sign to be 1+4, or 5. The slope of that line is-6/5. It is negative, and it falls from left to right.
What Is the Y Intercept?
The linear equation takes the form y = mx +b. It is called the slope-intercept form of the linear equation. Think of the relationship between x and y on any graph. At any point along the y axis, the value of x will equal zero. Therefore, substitute 0 for x, and y will equal b at the point where b crosses the y axis.
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