Find a missing coordinate using slope

key notes:

Concept of Slope

• The slope of a line tells how steep the line is.
• Formula for slope between two points (x₁,y₁) and (x2,y₂)):

m = y₂ − y₁ / x − x₁

where:

• m= slope
• (x₁,y₁) and (x₂,y₂) are two points on the line.

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Finding a Missing Coordinate

• If one coordinate is missing (either xxx or yyy), substitute the known values into the slope formula and solve for the unknown.

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Steps to Find a Missing Coordinate

• Write the slope formula:

m = y₂−y₁ / x₂−x₁

• Substitute the known values of m , x₁ , y₁ , x₂ , y₂
• Solve the equation for the missing coordinate.
• Check your answer by substituting back into the formula.

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Example 1: Missing y-coordinate

Given: Slope m = 2 , points (3,4) and (7,y₂)

2 = y₂−4 / 7−3

2 = y₂−4 / 4

Multiply both sides by 4:

8 = y₂ − 4

y₂ = 12

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Example 2: Missing x-coordinate

Given: Slope m=−3 , points (x₁,5) nd (8,2)

−3 = 2−5 / 8−x₁

−3 = −3 / 8−x₁

Multiply both sides by (8−x₁)

-3 (8−x₁) = −3

−24 + 3x₁ = −3

3x₁ = 21

x₁ = 7

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Key Tips

Always check for division by zero; slope is undefined if x₁ = x₂.

Pay attention to signs in subtraction.

Use parentheses when substituting negative numbers.

Slope can be positive, negative, zero, or undefined:

• Positive slope: line rises left to right.
• Negative slope: line falls left to right.
• Zero slope: horizontal line.
• Undefined slope: vertical line.

Learn with an example