Question - Calculating Slope and Y-Intercept from a Line Graph
Solution:
To find the slope of the line represented in the graph, you need to pick two points on the line that you can clearly identify the coordinates for. Then, use the formula for slope, which is:\[ slope (m) = \frac{change \, in \, y}{change \, in \, x} = \frac{y_2 - y_1}{x_2 - x_1} \]Looking at the graph, let's pick the two points where the line intersects the grid lines. One point could be at $$ (1, 1) $$ and another point could be at $$ (3, 7) $$.Now using these points:\[ x_1 = 1, y_1 = 1 \]\[ x_2 = 3, y_2 = 7 \]Let's calculate the slope:\[ slope (m) = \frac{7 - 1}{3 - 1} = \frac{6}{2} = 3 \]Next, to find the y-intercept (the point where the line crosses the y-axis), look at where the line intersects the y-axis. From the graph, it appears that the line crosses the y-axis at $$ (0, -1) $$. Therefore, the y-intercept (b) is -1.So the slope is 3, and the y-intercept is -1.
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