Last updated on August 5th, 2025
Understanding straight lines involves several key formulas. These include the slope of a line, the equation of a line in various forms, and other properties related to lines. In this topic, we will learn the formulas for straight lines as covered.
The study of straight lines involves several important formulas. Let’s learn the formulas to calculate the slope, equation, and other properties of straight lines.
The slope of a line is a measure of its steepness and direction. It is calculated using the formula:
Slope (m) = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are two distinct points on the line.
The equation of a line can be expressed in multiple forms.
Parallel lines have the same slope. Perpendicular lines have slopes that are negative reciprocals of each other.
If the slope of one line is m, the slope of a line perpendicular to it will be -1/m.
In math and real life, understanding straight lines is fundamental for analyzing and modeling linear relationships. Some key reasons include:
Students might find the math formulas for straight lines tricky.
Here are some tips and tricks to master these formulas:
Students often make errors when calculating or using straight line formulas. Here are some mistakes and ways to avoid them:
Find the slope of the line passing through the points (2, 3) and (5, 11)?
The slope is 8/3
To find the slope, use the formula: (y₂ - y₁) / (x₂ - x₁) = (11 - 3) / (5 - 2) = 8/3
Write the equation of the line with slope 2 passing through the point (1, 4)?
The equation is y = 2x + 2
Using the point-slope form: y - y₁ = m(x - x₁) y - 4 = 2(x - 1) y = 2x + 2
What is the slope of a line perpendicular to the line with equation y = -3x + 5?
The slope is 1/3
The slope of the given line is -3.
A line perpendicular to this will have a slope that is the negative reciprocal, which is 1/3.
Find the equation of the line parallel to y = -2x + 3 and passing through (3, 2)?
The equation is y = -2x + 8
Parallel lines have the same slope, so the slope is -2.
Using point-slope form: y - 2 = -2(x - 3) y = -2x + 8
Determine if the lines with equations 3x + 4y = 12 and 4x - 3y = 9 are perpendicular?
Yes, they are perpendicular
Convert to slope-intercept form to find slopes:
1st line: 4y = -3x + 12 → y = -3/4x + 3
2nd line: -3y = -4x + 9 → y = 4/3x - 3
are -3/4 and 4/3, negative reciprocals, so lines are perpendicular.
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
: He loves to play the quiz with kids through algebra to make kids love it.