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Determine if a Point Lies on a Line>
Determine if a Point Lies on a LineDetermine if a Point Lies on a Line
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Question 1 of 2
1. Question
Determine whether the points `(2,5)` and `(6,17)` lie on the line `y=3x-1`.Hint
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A point satisfies a line if it makes the equation true.Substitute the given points on the equation to see whether they lie on the line.Line: `y=3x+1`Point 1:`(``x_1``,``y_1``)` `=` `(``2``,``5``)` `y` `=` `3``x``-1` Equation of the line `5` `=` `3``(2)``-1` Plug in the values `5` `=` `6-1` Simplify `5` `=` `5` The equation is true Point 2:`(``x_2``,``y_2``)` `=` `U(``6``,``17``)` `y` `=` `3``x``-1` Equation of the line `17` `=` `3``(6)``-1` Plug in the values `17` `=` `18-1` Simplify `17` `=` `17` The equation is true Since both equations are true, both points lie on the line `y=3x-1``(2,5)` and `(6,17)` lie on the line -
Question 2 of 2
2. Question
Determine whether the points `(3,4)` and `(2,1)` lie on the line `y=-x+3`.Hint
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A point satisfies a line if it makes the equation true.Substitute the given points on the equation to see whether they lie on the line.Line: `y=-x+3`Point 1:`(``x_1``,``y_1``)` `=` `(``3``,``4``)` `y` `=` `-``x``+3` Equation of the line `4` `=` `-``(3)``+3` Plug in the values `4` `=` `-3+3` Simplify `4` `!=` `0` The equation is false Therefore the point `(3,4)` does not lie on the line `y=-x+3`Point 2:`(``x_2``,``y_2``)` `=` `U(``2``,``1``)` `y` `=` `-``x``+3` Equation of the line `1` `=` `-``(2)``+3` Plug in the values `1` `=` `-2+3` Simplify `1` `=` `1` The equation is true Only the point `(2,1)` lies on the line `y=-x+3``(2,1)` lies on the line
Quizzes
- Distance Between Two Points 1
- Distance Between Two Points 2
- Distance Between Two Points 3
- Midpoint of a Line 1
- Midpoint of a Line 2
- Midpoint of a Line 3
- Gradient of a Line 1
- Gradient of a Line 2
- Gradient Intercept Form: Graph an Equation 1
- Gradient Intercept Form: Graph an Equation 2
- Gradient Intercept Form: Write an Equation 1
- Determine if a Point Lies on a Line
- Graph Linear Inequalities 1
- Graph Linear Inequalities 2
- Convert Between General Form and Gradient Intercept Form 1
- Convert Between General Form and Gradient Intercept Form 2
- Point Gradient and Two Point Formula 1
- Point Gradient and Two Point Formula 2
- Parallel Lines 1
- Parallel Lines 2
- Perpendicular Lines 1
- Perpendicular Lines 2