Line Equation from Point and Gradient

Find the Line Equation

Given Information:

Point: (x₁, y₁)

Gradient (m): ?

Line Equation Forms:

Point-slope form: y - y₁ = m(x - x₁)

Slope-intercept form: y = mx + c

Calculate the Line Equation

Step 1: Identify the point and gradient

Identify the x and y values for the point and the gradient:

Point:

x₁ = ?, y₁ = ?

Gradient:

m = ?

Step 2: Write the equation in point-slope form

Use the formula: y - y₁ = m(x - x₁)

y - ? = ?(x - ?)

Enter the equation in point-slope form:

y - = (x - )

Step 3: Expand the equation

Expand the point-slope form by multiplying out the brackets:

y - ? = ?(x - ?)

y - ? = ?x - ?

Enter the expanded equation:

y - = x -

Step 4: Rearrange to slope-intercept form (y = mx + c)

Rearrange the equation to get y on its own:

y - ? = ?x - ?

y = ?x - ? + ?

Enter the equation in slope-intercept form (y = mx + c):

y = x +

Step 5: Write the equation in general form

Convert from y = mx + c to ax + by + c = 0

From y = ?x + ?

Rearrange to get: ?x - y + ? = 0

Enter the equation in the form ax + by + c = 0:

x + y + = 0

Final Answer

The equation of the line is:

y - y₁ = m(x - x₁)

y = mx + c

ax + by + c = 0

Your Progress:

Line Equation Calculator