Linear Equation Formula
The equation of a line can be written in a form that makes the slope obvious and allows you to draw the line without any computation. If students are comfortable with solving a simple two-step linear equation, they can write linear equations in slope-intercept form. The slope-intercept form of a linear equation is y = mx + b. In the equation, x and y are the variables. The numbers m and b give the slope of the line [m] and the value of y when x is 0 [b]. The value of y when x is 0 is called the y-intercept because [0,y] is the point at which the line crosses the y-axis.
You can draw the line for an equation matching this linear formula by plotting [0,b], then using m to find another point. For example, if m is 1/2, you can interpret that as a difference in 1 among y coordinates for every difference in 2 among x coordinates [that is, [y2 – y1]/[x2 – x1] = 1/2]. Count +2 on the x-axis, then +1 on the y-axis to get to another point: [2, b + 1].
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