Point Slope Form 2
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 7 questions completed
Questions:
- 1
- 2
- 3
- 4
- 5
- 6
- 7
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- Answered
- Review
-
Question 1 of 7
1. Question
Find the equation of a line with the slope `m=-1/2` and passing through the point `(5,-3)`.Hint
Help VideoCorrect
Keep Going!
Incorrect
Point Gradient Form: `y-``y_1``=``m``(x-``x_1``)`
- `m` is the gradient of the line
- `(x_1,y_1)` is a point that lies on the line
Substitute the given gradient and point into the formula.Point: `(x_1,y_1)=(5,-3)`Gradient: `m=-1/2``y-``y_1` `=` `m``(x-``x_1``)` Point-Gradient Formula `y-``(-3)` `=` `(-1/2)``(x-``5``)` Plug in the values `y+3` `=` `-1/2x+5/2` `2y+6` `=` `-x+5` Multiply both sides by `2` `2y+6` `+x-5` `=` `-x+5` `+x-5` Add `x-5` to both sides `x+2y+1` `=` `0` Simplify `x+2y+1=0` -
Question 2 of 7
2. Question
Find the equation of a line with the slope `m=2` and passing through the point `(-5,-6).`
Correct
Keep Going!
Incorrect
Point Slope Form: `y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))`
- `color(tomato)(m)` is the slope of the line
- `(color(royalblue)(x_1,y_1))` is a point that lies on the line
Substitute the given slope and point into the formula.Point: `(x_1,y_1)=(-5,-6)`Slope: `m=2``y- color(royalblue)(y_1)` `=` `color(tomato)(m)(x- color(royalblue)(x_1))` Point Slope formula `y- color(royalblue)(-6)` `=` `color(tomato)((2))(x- color(royalblue)((-5)))` Plug in the values `y+6` `=` `2x + 10` `y+6 color(crimson)(-y-6)` `=` `2x + 10 color(crimson)(-y-6)` Add `-y-6` to both sides `0` `=` `2x-y+4` Simplify `2x-y+4` `=` `0` `2x-y+4=0` -
Question 3 of 7
3. Question
Find the equation of a line with the slope `m=-1/2` and passing through the point `(2,3)`.
Correct
Keep Going!
Incorrect
Point Slope Form: `y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))`
- `color(tomato)(m)` is the slope of the line
- `(color(royalblue)(x_1,y_1))` is a point that lies on the line
Substitute the given slope and point into the formula.Point: `(x_1,y_1)=(2,3)`Slope: `m=-1/2``y- color(royalblue)(y_1)` `=` `color(tomato)(m)(x- color(royalblue)(x_1))` Point Slope formula `y- color(royalblue)(3)` `=` `color(tomato)((-1/2))(x- color(royalblue)((2)))` Plug in the values `y-3` `=` `-1/2x + 1` `2y-6` `=` `x – 2` Multiply both sides by `-2` `-2y+6 color(crimson)(+2y-6)` `=` `x – 2 color(crimson)(+2y-6)` Add `2y-6` to both sides `0` `=` `x+2y-8` Simplify `x+2y-8` `=` `0` `x+2y-8=0` -
Question 4 of 7
4. Question
Find the equation of a line passing through the points `(-1,-7)` and `(1,3)`.
Correct
Keep Going!
Incorrect
Two Point Formula
`(y-color(darkviolet)(y_1))/(x-color(forestgreen)(x_1))=(color(darkviolet)(y_2)-color(darkviolet)(y_1))/(color(forestgreen)(x_2)-color(forestgreen)(x_1))`Solve for the slope first using the given points.Point: `(color(forestgreen)(x_1),color(darkviolet)(y_1))=(color(forestgreen)(-1), color(darkviolet)(-7))`Point: `(color(forestgreen)(x_2),color(darkviolet)(y_2))=(color(forestgreen)(1), color(darkviolet)(3))``(y-color(darkviolet)(y_1))/(x-color(forestgreen)(x_1))` `=` `(color(darkviolet)(y_2)-color(darkviolet)(y_1))/(color(forestgreen)(x_2)-color(forestgreen)(x_1))` Two Point Formula `(y-color(darkviolet)(-7))/(x-color(forestgreen)(-1))` `=` `(color(darkviolet)(3)-color(darkviolet)(-7))/(color(forestgreen)(1)-color(forestgreen)(-1))` Plug in the values `(y+7)/(x+1)` `=` `(10)/2` `(y+7)/(x+1)` `=` `5` `y+7` `=` `5x+5` Multiply both sides by `x+1` `y+7 color(crimson)(-2)` `=` `5x+5 color(crimson)(-2)` Add `-2` to both sides `y` `=` `5x+3` Simplify `y=5x+3` -
Question 5 of 7
5. Question
Find the equation of a line passing through the points `(0,2)` and `(1,-2)`.
Correct
Keep Going!
Incorrect
Two Point Formula
`(y-color(darkviolet)(y_1))/(x-color(forestgreen)(x_1))=(color(darkviolet)(y_2)-color(darkviolet)(y_1))/(color(forestgreen)(x_2)-color(forestgreen)(x_1))`Solve for the slope first using the given points.Point: `(color(forestgreen)(x_1),color(darkviolet)(y_1))=(color(forestgreen)(0), color(darkviolet)(2))`Point: `(color(forestgreen)(x_2),color(darkviolet)(y_2))=(color(forestgreen)(1), color(darkviolet)(-2))``(y-color(darkviolet)(y_1))/(x-color(forestgreen)(x_1))` `=` `(color(darkviolet)(y_2)-color(darkviolet)(y_1))/(color(forestgreen)(x_2)-color(forestgreen)(x_1))` Two Point Formula `(y-color(darkviolet)(2))/(x-color(forestgreen)(0))` `=` `(color(darkviolet)(-2)-color(darkviolet)(2))/(color(forestgreen)(1)-color(forestgreen)(0))` Plug in the values `(y-2)/(x)` `=` `(-4)/1` `(y-2)/x` `=` `-4` `y-2` `=` `-4x` Multiply both sides by `x` `y-2 color(crimson)(+2)` `=` `-4x color(crimson)(+2)` Add `2` to both sides `y` `=` `-4x+2` Simplify `y=-4x+2` -
Question 6 of 7
6. Question
Find the equation of a line passing through the points `(-6,8)` and `(4,8)`.
Correct
Keep Going!
Incorrect
Two Point Formula
`(y-color(darkviolet)(y_1))/(x-color(forestgreen)(x_1))=(color(darkviolet)(y_2)-color(darkviolet)(y_1))/(color(forestgreen)(x_2)-color(forestgreen)(x_1))`Solve for the slope first using the given points.Point: `(color(forestgreen)(x_1),color(darkviolet)(y_1))=(color(forestgreen)(-6), color(darkviolet)(8))`Point: `(color(forestgreen)(x_2),color(darkviolet)(y_2))=(color(forestgreen)(4), color(darkviolet)(8))``(y-color(darkviolet)(y_1))/(x-color(forestgreen)(x_1))` `=` `(color(darkviolet)(y_2)-color(darkviolet)(y_1))/(color(forestgreen)(x_2)-color(forestgreen)(x_1))` Two Point Formula `(y-color(darkviolet)(8))/(x-color(forestgreen)(-6))` `=` `(color(darkviolet)(8)-color(darkviolet)(8))/(color(forestgreen)(4)-color(forestgreen)(-6))` Plug in the values `(y-8)/(x+6)` `=` `0/(4+6)` `(y-8)/(x+6)` `=` `0` `y-8` `=` `0` `y-8 color(crimson)(+8)` `=` `0 color(crimson)(+8)` Add `8` to both sides `y` `=` `8` Simplify `y=8` -
Question 7 of 7
7. Question
Find the equation of a line passing through the points `(1,8)` and `(-2,2)`.Hint
Help VideoCorrect
Well Done!
Incorrect
Point Gradient Form: `y-``y_1``=``m``(x-``x_1``)`
- `m` is the gradient of the line
- `(x_1,y_1)` is a point that lies on the line
Gradient Formula
$$m=\frac{\color{#9a00c7}{y_2}-\color{#9a00c7}{y_1}}{\color{#00880a}{x_2}-\color{#00880a}{x_1}}$$Solve for the gradient first using the given points.Point: `(``x_1`,`y_1``)=(``1`,`8``)`Point: `(``x_2`,`y_2``)=(``-2`,`2``)``m` `=` $$\frac{\color{#9a00c7}{y_2}-\color{#9a00c7}{y_1}}{\color{#00880a}{x_2}-\color{#00880a}{x_1}}$$ Gradient Formula `=` $$\frac{\color{#9a00c7}{2}-\color{#9a00c7}{8}}{\color{#00880a}{-2}-\color{#00880a}{1}}$$ Plug in the Values `=` `(-6)/(-3)` `m` `=` `2` Substitute the calculated gradient and one point into the Point-Gradient Formula.Point: `(x_1,y_1)=(1,8)`Gradient: `m= 2``y-``y_1` `=` `m``(x-``x_1``)` Point-Gradient Formula `y-``8` `=` `(2)``(x-``1``)` Plug in the values `y-8` `=` `2x-2` `y-8` `+8` `=` `2x-2` `+8` Add `8` to both sides `y` `=` `2x+6` Simplify `y=2x+6`
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
- Slope of a Line 1
- Slope of a Line 2
- Slope Intercept Form: Graph an Equation 1
- Slope Intercept Form: Graph an Equation 2
- Slope Intercept Form: Write an Equation 1
- Graph Linear Inequalities 2
- Convert Standard Form and Slope Intercept Form 1
- Convert Standard Form and Slope Intercept Form 2
- Point Slope Form 1
- Point Slope Form 2
- Parallel Lines 1
- Parallel Lines 2
- Perpendicular Lines 1
- Perpendicular Lines 2
- Graph Linear Inequalities 1