How is the linear equation related to the linear graph? - Answers

A linear equation is similar to a linear graph in that key data from the equation is clearly visible on the graph. A linear equation of y = 4x + 5 shows us that the y-intercept (or "b") is +5. This is where our line crosses the y-axis, and provides us with the information that the point (0, 5) exists on our line, making it the easiest point to draw on our graph every time! The equation also shows us that there is a slope (or "m") of 4. This means we must do the long-form of slope, which is "rise over run" or "change in y, divided by change in x". A slope of 4 is written as 4/1, or "four over one", showing we 'rise' 4 units on our graph, and 'run' 1 unit...clearly showing a slope of 4.