Slope and Y-intercept of a Line

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

• Inclination of a Line
• Slope of a Line
• Intercepts Made by a Straight Line on Axes
• Slope of the Line Joining Two Points
• Equation of a Straight Line
• Point-slope Form of a Line
• Two-point Form of a Line
• Equally Inclined Lines
• Slope and Y-intercept of a Line
• Condition of Perpendicularity of Two Straight Lines
• Condition of parallelism
• Problems on Condition of Perpendicularity
• Worksheet on Slope and Intercepts
• Worksheet on Slope Intercept Form
• Worksheet on Two-point Form
• Worksheet on Point-slope Form
• Worksheet on Collinearity of 3 Points
• Worksheet on Equation of a Straight Line

10th Grade Math

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