Point Slope Form 2

Topics

Algebra 2

Linear Equations and Graphs

Point Slope Form

Point Slope Form 2

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Question 1 of 7

Find the equation of a line with the slope

m = - \frac{1}{2}

$m=-1/2$ and passing through the point

(5, - 3)

$(5,-3)$ .

1. $x + 2 y - 1 = 0$ $x+2y-1=0$
2. $x + 2 y = 0$ $x+2y=0$
3. $x + 2 y - 2 = 0$ $x+2y-2=0$
4. $x + 2 y + 1 = 0$ $x+2y+1=0$

Question 2 of 7

Find the equation of a line with the slope $m=2$ and passing through the point $(-5,-6).$

1. $2x+3y+4=0$
2. $2x+2y+4=0$
3. $2x-y-4=0$
4. $2x-y+4=0$

Question 3 of 7

Find the equation of a line with the slope $m=-1/2$ and passing through the point $(2,3)$ .

1. $x+2y-8=0$
2. $x+2y-6=0$
3. $2x+y-4=0$
4. $x+2y=0$

Question 4 of 7

Find the equation of a line passing through the points $(-1,-7)$ and $(1,3)$ .

1. $y=2x-5$
2. $y=3x+5$
3. $y=5x+3$
4. $y=-3x-8$

Question 5 of 7

Find the equation of a line passing through the points $(0,2)$ and $(1,-2)$ .

1. $y=2x$
2. $y=4x+6$
3. $y=-2x+1$
4. $y=-4x+2$

Question 6 of 7

Find the equation of a line passing through the points $(-6,8)$ and $(4,8)$ .

1. $y=8$
2. $y=8x$
3. $y=2x+8$
4. $y=8x+4$

Question 7 of 7

Find the equation of a line passing through the points

$(1,8)$ and

$(-2,2)$ .

1. $y=2x+4$
2. $y=3x+6$
3. $y=2x+10$
4. $y=2x+6$

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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

$y=2x+6$

$y -$ $y-$ $y_{1}$ $y_1$	$=$ $=$	$m$ $m$ $(x -$ $(x-$ $x_{1}$ $x_1$ $)$ $)$	Point-Gradient Formula

$y -$ $y-$ $(- 3)$ $(-3)$	$=$ $=$	$(- \frac{1}{2})$ $(-1/2)$ $(x-$ $5$ $)$	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

$y- color(royalblue)(y_1)$	$=$	$color(tomato)(m)(x- color(royalblue)(x_1))$	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
$2x-y+4$	$=$	$0$

$y- color(royalblue)(y_1)$	$=$	$color(tomato)(m)(x- color(royalblue)(x_1))$	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
$x+2y-8$	$=$	$0$

$(y-color(darkviolet)(y_1))/(x-color(forestgreen)(x_1))$	$=$	$(color(darkviolet)(y_2)-color(darkviolet)(y_1))/(color(forestgreen)(x_2)-color(forestgreen)(x_1))$	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

$(y-color(darkviolet)(y_1))/(x-color(forestgreen)(x_1))$	$=$	$(color(darkviolet)(y_2)-color(darkviolet)(y_1))/(color(forestgreen)(x_2)-color(forestgreen)(x_1))$	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

Point Slope Form 2

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Quiz summary

Information

1. Question

Hint

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Point Gradient Form: $y -$ $y-$ $y_{1}$ $y_1$ $=$ $=$ $m$ $m$ $(x -$ $(x-$ $x_{1}$ $x_1$ $)$ $)$

2. Question

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Point Slope Form: $y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))$

3. Question

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Point Slope Form: $y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))$

4. Question

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Two Point Formula

5. Question

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Two Point Formula

6. Question

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Two Point Formula

7. Question

Hint

Well Done!

Point Gradient Form: $y-$ $y_1$ $=$ $m$ $(x-$ $x_1$ $)$

Gradient Formula

Quizzes

Point Slope Form 2

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Quiz summary

Information

1. Question

Hint

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Point Gradient Form: y-y−y-y1y1y_1===mmm(x-(x−(x-x1x1x_1)))

2. Question

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Point Slope Form: y-y1=m(x-x1)y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))

3. Question

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Point Slope Form: y-y1=m(x-x1)y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))

4. Question

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Two Point Formula

5. Question

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Two Point Formula

6. Question

Keep Going!

Two Point Formula

7. Question

Hint

Well Done!

Point Gradient Form: y-y-y1y_1==mm(x-(x-x1x_1))

Gradient Formula

Quizzes

Point Gradient Form: $y -$ $y-$ $y_{1}$ $y_1$ $=$ $=$ $m$ $m$ $(x -$ $(x-$ $x_{1}$ $x_1$ $)$ $)$

Point Slope Form: $y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))$

Point Slope Form: $y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))$

Point Gradient Form: $y-$ $y_1$ $=$ $m$ $(x-$ $x_1$ $)$