We will learn how to find the slope and y-intercept of a line.
Consider the following steps to find the slope and y-intercept of a given line:
Step I: Convert the given equation of the line in the slope-intercept form y = mx + c.
Step II: Then, the co-efficient of x is slope (m) and the constant term term with its proper sign is y-intercept (c).
Solved examples on slope and y-intercept of a line:
1. Find the slope and y-intercept of the line 2x - 3y - 4 = 0.
Solution:
Given equation is 2x - 3y - 4 = 0
⟹ -3y = -2x + 4
⟹ y = \(\frac{2}{3}\)x - \(\frac{4}{3}\)
Therefore, the slope (m) of the given line = \(\frac{2}{3}\) and its y-intercept (c) = - \(\frac{4}{3}\)
2. Find the slope and y-intercept of the line 3x + 2y + 4 =
0
Solution:
First we need to express the given equation in the form y = mx + c.
Given equation is 3x + 2y + 4 = 0
⟹ 2y = -3x - 4
⟹ y = -\(\frac{3}{2}\)x - \(\frac{4}{2}\)
⟹ y = -\(\frac{3}{2}\)x - 2
Therefore, the slope (m) of the given line = -\(\frac{3}{2}\) and its y-intercept (c) = - 2
3. Find the slope and y-intercept of the line y = 4
Solution:
First we need to express the given equation in the form y = mx + c.
Given equation is y = 4
⟹ y = 0x + 4
Therefore, the slope (m) of the given line = 0 and its y-intercept (c) = 4
4. Find the slope and y-intercept of the line 3x - 4y = 5
Solution:
First we need to express the given equation in the form y = mx + c.
Given equation is 3x - 4y = 5
⟹ -4y = -3x + 5
⟹ y = \(\frac{-3}{-4}\)x + \(\frac{5}{-4}\)
⟹ y = \(\frac{3}{4}\)x - \(\frac{5}{4}\)
Therefore, the slope (m) of the given line = \(\frac{3}{4}\) and its y-intercept (c) = - \(\frac{5}{4}\)
● Equation of a Straight Line
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