Question - Calculating Slope and Y-Intercept from Graph
Solution:
To find the slope and y-intercept of the line in the graph, we can use the following steps:**Slope:** The slope of a line is calculated by the rise over run. This means you need to determine how many units the line goes up (or down) for each unit it goes to the right. Looking at the graph, if we take two points on the line, for example, the point where it crosses the y-axis (the y-intercept) and any other point on the line, we can calculate the slope.From the graph, it looks like the line crosses the y-intercept at (0, 3) and goes through another point at (2, 7).Slope $$ m = \frac{{change \, in \, y}}{{change \, in \, x}} = \frac{{y_2 - y_1}}{{x_2 - x_1}} $$So here, with our points (0, 3) and (2, 7):$$ m = \frac{{7 - 3}}{{2 - 0}} $$$$ m = \frac{4}{2} $$$$ m = 2 $$The slope of the line is 2.**y-intercept:**The y-intercept is the point where the line crosses the y-axis. By inspecting the graph, the line crosses the y-axis at the point (0, 3).So the y-intercept is 3.Putting it all together, the slope is 2, and the y-intercept is 3.
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