The point-slope form is a method used in algebra to write the equation of a line when you know the slope of the line and the coordinates of one point on the line. This form is particularly useful for quickly writing the equation of a line in linear relationships.
Formula for Point-Slope Form
The point-slope form of a line is given by the formula: y – y1 = m(x – x1). In this formula:
- ‘m’ represents the slope of the line.
- ‘(x1, y1)’ are the coordinates of the known point on the line.
- ‘(x, y)’ are the coordinates of any other point on the line.
How to Use Point-Slope Form
- Start with the known slope of the line and the coordinates of a known point on the line.
- Substitute the known values into the formula: y – y1 = m(x – x1).
- Rearrange the formula as needed to express it in different forms, such as slope-intercept form (y = mx + b).
Example 1
Write the equation of a line with a slope of 3 that passes through the point (2, -1).
Using the point-slope form: y – (-1) = 3(x – 2). Simplifying, y + 1 = 3x – 6, which leads to y = 3x – 7.
Example 2
Write the equation of a line with a slope of -2 that passes through the point (4, 1).
Using the point-slope form: y – 1 = -2(x – 4). Simplifying, y – 1 = -2x + 8, which leads to y = -2x + 9.
The Most Popular Topics:
- Corresponding angles
- Adjacent angles
- Congruent angles
- Complementary angles
- How to multiply fractions – multiplying fractions
- How to divide fractions – dividing fractions
- How to add fractions – adding fractions
- How to subtract fractions – subtracting fractions
- How to simplify fractions – simplifying fractions
- Midpoint, midpoint formula
- Quadratic formula
- Quadratic equation
- Median – what is the median in math?
- How to find median?
- Distributive property
- Associative property
- Commutative property
- Quotient – what is a quotient?
- Quotient rule
- System of equations
- Solving system of equations
- Linear equations
- Solving equations
- Slope
- Slope formula
- Slope calculator
- Point slope formula
- Slope intercept form
- How to find slope?
- Convert fraction to decimal
- Factors of a number
- Point slope form
- Slope equation
- Domain and range
- Domain – what is domain in math?
- How to find the domain of a function?
- How to find domain and range?
- Polynomial
- Polynomial long division
- Polynomial division – dividing polynomials
- Degree of polynomial
- Factoring polynomials – how to factor polynomials?
- Perpendicular lines
- Parabola equation
- Isosceles triangle
- Perimeter of triangle
- Scalene triangle
- Obtuse triangle
- Acute triangle
- Right triangle
- Trapezoid area formula
- What is a trapezoid?
- Isosceles trapezoid
- Rectangle
- Area of a rectangle
- Perimeter of a rectangle – how to find perimeter of a rectangle?
- Pythagorean theorem
- Vertex – how to find vertex?
- Vertex form
- Vertex formula
- How to find square root of a number?
Return to MathQuadrum.com from Point slope form home for more topics on mathematics