Question - Graphing a Line Using Point-Slope Form
Solution:
To graph the line given by the equation $$ y - 2 = \frac{-2}{5}(x - 4) $$, you can follow these steps:1. **Identify the slope and y-intercept:** The equation is in point-slope form, $$ y - y_1 = m(x - x_1) $$, where $$ m $$ is the slope and $$ (x_1, y_1) $$ is a point on the line. In this case, the slope ($$ m $$) is $$ \frac{-2}{5} $$ and the point on the line is (4, 2).2. **Plot the point on the graph:** Begin by plotting the point (4, 2) on your graph paper. This will be a point through which the line passes.3. **Use the slope to find another point:**The slope $$ \frac{-2}{5} $$ means you move 2 units down and 5 units to the right from the point (4, 2) to find another point on the line. You could also move 2 units up and 5 units to the left if you wish to go in the opposite direction.4. **Draw the line:** Connect the two points with a straight line. This line will extend infinitely in both directions.It's important to be precise and to plot points correctly. If you have graph paper, use a ruler to ensure that the line passes through the points accurately and extends across the grid.
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