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Slope of the Graph of y = mx + c
Here we will learn how to solve the slope of the graph of y = mx + c.
The graph of y = mx + c is a straight line joining the points (0, c) and (\(\frac{-c}{m}\), 0).
Let M = (\(\frac{-c}{m}\), 0) and N = (0, c) and ∠NMX = θ.
Then, tan θ is called the slope of the line which is the graph of y = mx + c.
Now, ON = c and OM = \(\frac{c}{m}\).
Therefore, in the right-angled ∆MON, tan θ = \(\frac{ON}{OM}\) = \(\frac{c}{\frac{c}{m} }\) = m.
Thus, the slope of the line which is the graph of y = mx + c is m
And m is equal to the tangent of the angle that the line makes with the positive direction of the x-axis.
Solved examples on slope of the graph of y = mx + c:
1. What is the slope of the line which makes 60° with the positive direction of the x-axis?
Solution:
The slope = tan 60° = √3
2. What is the slope of the line which is the graph of 2x – 3y + 5 = 0?
Solution:
Here, 2x – 3y + 5 = 0
⟹ 3y = 2x + 5
⟹ y = \(\frac{2}{3}\)x + \(\frac{5}{3}\).
Comparing with y = mx + c, we have m = \(\frac{2}{3}\).
Therefore, the slope of the line is \(\frac{2}{3}\).
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