How do I do this? Graph the line containing the given pair of the points and find the slope. (2,4), (-6,-4).
slope = m = (-4-4)/(-6-2) = -8/-8 = 1
y = m x + b
y = 1 x + b
4 = 2 + b
b = 2
so
y = x + 2 is our line
check if it goes through second point
-4 = -6 + 2 yes, check
To graph the line containing the given pair of points and find the slope, you can follow these steps:
1. Plot the given points on a coordinate plane. For the first point (2,4), locate the point with coordinates (2,4) on the graph by going 2 units to the right on the x-axis and 4 units up on the y-axis. Mark this point on the graph. Similarly, for the second point (-6,-4), locate the point with coordinates (-6,-4) by going 6 units to the left on the x-axis and 4 units down on the y-axis. Mark this point on the graph as well.
2. Now, draw a straight line through the two points you plotted. This line represents the graph of the equation connecting the given pair of points.
3. To find the slope, recall that the slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) is calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Plug in the coordinates of the two points you have: (2,4) and (-6,-4).
Substituting those values into the formula, we have:
m = (-4 - 4) / (-6 - 2)
= -8 / -8
= 1
Therefore, the slope of the line passing through the given pair of points is 1.
That's it! You have now graphed the line containing the given pair of points and found its slope.