wintry, snow, backcountry skiiing @ Pixabay

The slope of the line containing points  m(1, 3) and n(5, 0) is equal to the slope of the line connecting these two points. In other words, it’s a straight line through the origin with slope  3/5 or 1/2. The slope is a ratio of the vertical change in y-values to the horizontal change in x-values. The more “up” or positive value you go on your graph, then the higher up you are going vertically and vice versa as well for negative values. Slope can be illustrated by measuring two points along a line with coordinates (x0,  y0) and (x0 + Δx, y0 +  Δy). Let’s say that we start from point A(−20,-35), where there is an  initial displacement of 20 units both horizontally and vertically from the origin; what would happen if we went upwards one unit? As seen here: Obviously this will result in an increase in the y-value of one. The ratio between Δy and  Δx is constant, or in other words slope will not change since they are proportional to each other. This proves that we have a positive slope! If this were negative then it would be going down vertically as well for whatever x unit you go horizontally, and vice versa with positives slopes. Slope can be interpreted as “rise over run” which means how many units an object goes up per distance that it moves along the horizontal axis (change). All lines on a graph have an infinite number of slopes because their values vary depending upon where they intersect any vertical line drawn through them; however, when looking at two points plotted out on a plane


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