![]() ![]() When x = 0, the corresponding y-value is the y-intercept. For instance, an exercise might deal with how the population grows in a certain city, with the population increasing by a certain fixed amount every year. Often, linear-equation word problems deal with changes over the course of time the equations will deal with how much something changes as time passes. While this doesn't necessarily graph as easily as "three up and five over", it can be a more useful way of viewing things when you're doing word problems. In other words, for every one unit that x moves over to the right, y goes up by three-fifths of a unit. But we could also view this slope as a fraction over 1: This means that, starting at any point on this line, you can get to another point on the line by going up 3 units and then going to the right 5 units. For instance, in the line y = ( 3/5 )x – 2, the slope is m = 3/5. We have seen that the slope of a line measures how much the value of y changes for every so much that the value of x changes. In this lesson, we are going to look at the "real world" meanings that slope and y-intercept can have. Graphing from this format can be quite straightforward, particularly if the values of "m" and "b" are relatively simple numbers (such as 2 or –4.5, rather than 17/19 or 1.67385). This useful form of the line equation is sensibly named the "slope-intercept form". In the equation of a straight line (when the equation is written as "y = mx + b"), the slope is the number "m" that is multiplied on the x, and "b" is the y-intercept, where the line crosses the y-axis. ![]()
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