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Calculate point-slope form, slope-intercept form, and standard form of linear equations. Perfect for algebra, linear functions, and graphing applications.
Comprehensive linear equation calculations with detailed explanations
Calculate equations from point and slope
Calculate equations from two points
Convert to y = mx + b form
Convert to Ax + By + C = 0 form
Understanding linear equation forms and algebraic transformations
Choose from two points, point and slope, slope-intercept, or intercepts.
Input coordinates, slope, or intercept values as required.
Receive point-slope, slope-intercept, and standard form equations.
y - y₁ = m(x - x₁)
y = mx + b
Ax + By + C = 0
m = (y₂ - y₁)/(x₂ - x₁)
Common linear equation calculations and their practical applications
Result: y - 3 = 2(x - 2)
Result: y - 2 = 3(x - 1)
Result: y - 32 = 1.8(x - 0)
Result: y - 10 = 5(x - 0)
Common questions about point-slope form calculations
Point-slope form is a linear equation format: y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope. It's useful when you know a point and the slope of a line.
To convert y - y₁ = m(x - x₁) to y = mx + b, solve for y: y = mx - mx₁ + y₁. The y-intercept b = y₁ - mx₁.
Point-slope form (y - y₁ = m(x - x₁)) uses a specific point and slope, while slope-intercept form (y = mx + b) uses the slope and y-intercept. Both represent the same line but in different formats.
The slope formula is m = (y₂ - y₁)/(x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are two points on the line. This gives you the rate of change between the points.
Use point-slope form when you know a specific point on the line and the slope. It's particularly useful for writing equations of lines that pass through given points.
To convert to standard form Ax + By + C = 0, rearrange the equation so all terms are on one side and coefficients are integers. For example, y = 2x - 1 becomes 2x - y - 1 = 0.
If you know the intercepts (a, 0) and (0, b), you can use the intercept form: x/a + y/b = 1, or find the slope using m = -b/a and use point-slope form with one of the intercepts.
Yes, you can use any point (x₁, y₁) that lies on the line. Different points will give different-looking equations, but they all represent the same line.
For vertical lines (undefined slope), use x = a. For horizontal lines (slope = 0), use y = b. Point-slope form works for all other lines with defined slopes.
Point-slope form is great for writing equations from a point and slope. Slope-intercept form is best for graphing and finding intercepts. Standard form is useful for systems of equations and finding perpendicular lines.
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