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 \(\frac{2}{3}\).
From Slope of the graph of y = mx + c to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
May 18, 24 02:59 PM
May 12, 24 06:28 PM
May 12, 24 06:23 PM
May 12, 24 06:09 PM
May 12, 24 04:59 PM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.