Point Slope Form 1

Topics

Algebra 2

Linear Equations and Graphs

Point Slope Form

Point Slope Form 1

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Question 1 of 8

Find the equation of a line with the slope

$m=2/5$ and passing through the point

$(-2,4)$ .

1. $2x-5y+24=0$
2. $2x-5y-24=0$
3. $2x-5y=0$
4. $2x-5y+16=0$

Question 2 of 8

Find the equation of a line with the slope $m=-1$ and passing through the point $(4,-3).$

1. $x - y -24=0$
2. $x + y + 7=0$
3. $x + y -1=0$
4. $x + y -1=0$

Question 3 of 8

Find the equation of a line with the slope $m=-2$ and passing through the point $(3,5).$

1. $2x+y-11=0$
2. $2x+y-1=0$
3. $2x-y-11=0$
4. $x-2y-7=0$

Question 4 of 8

Find the equation of a line with the slope $m=0$ and passing through the point $(4,-2).$

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

Question 5 of 8

Find the equation of a line passing through the points

$(0,2)$ and

$(2,-4)$ .

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

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Two Point Formula

$\frac{y-\color{#9a00c7}{y_1}}{x-\color{#00880a}{x_1}}=\frac{\color{#9a00c7}{y_2}-\color{#9a00c7}{y_1}}{\color{#00880a}{x_2}-\color{#00880a}{x_1}}$

Solve for the gradient first using the given points.

Point:

$($ $x_1$ , $y_1$

$)=($ $0$ , $2$

$)$

Point:

$($ $x_2$ , $y_2$

$)=($ $2$ , $-4$

$)$

$\frac{y-\color{#9a00c7}{y_1}}{x-\color{#00880a}{x_1}}$	$=$	$\frac{\color{#9a00c7}{y_2}-\color{#9a00c7}{y_1}}{\color{#00880a}{x_2}-\color{#00880a}{x_1}}$	Two Point Formula

$\frac{y-\color{#9a00c7}{2}}{x-\color{#00880a}{0}}$	$=$	$\frac{\color{#9a00c7}{-4}-\color{#9a00c7}{2}}{\color{#00880a}{2}-\color{#00880a}{0}}$	Plug in the values

$(y-2)/(x)$	$=$	$(-6)/2$

$(y-2)/x$	$=$	$-3$

$y-2$	$=$	$-3x$	Multiply both sides by $x$
$y-2$ $+2$	$=$	$-3x$ $+2$	Add $2$ to both sides
$y$	$=$	$-3x+2$	Simplify

$y=-3x+2$

Question 6 of 8

Find the equation of a line passing through the points

$(1,5)$ and

$(-4,-10)$ .

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

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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:

$($ $x_1$ , $y_1$

$)=($ $1$ , $5$

$)$

Point:

$($ $x_2$ , $y_2$

$)=($ $-4$ , $-10$

$)$

$m$	$=$	$\frac{\color{#9a00c7}{y_2}-\color{#9a00c7}{y_1}}{\color{#00880a}{x_2}-\color{#00880a}{x_1}}$	Gradient Formula

	$=$	$\frac{\color{#9a00c7}{-10}-\color{#9a00c7}{5}}{\color{#00880a}{-4}-\color{#00880a}{1}}$	Plug in the Values

	$=$	$(-15)/(-5)$

$m$	$=$	$3$

Substitute the calculated gradient and one point into the Point-Gradient Formula.

Point:

$(x_1,y_1)=(1,5)$

Gradient:

$m= 3$

$y-$ $y_1$	$=$	$m$ $(x-$ $x_1$ $)$	Point-Gradient Formula
$y-$ $5$	$=$	$(3)$ $(x-$ $1$ $)$	Plug in the values
$y-5$	$=$	$3x-3$
$y-5$ $+5$	$=$	$3x-3$ $+5$	Add $5$ to both sides
$y$	$=$	$3x+2$	Simplify

$y=3x+2$

Question 7 of 8

Find the equation of a line passing through the points $(0,0)$ and $(-4,3)$ .

1. $y=-3x$
2. $y=-3x-4$
3. $y=(-3x)/4$
4. $y=-3x+4$

Question 8 of 8

Find the equation of a line passing through the points $(0,-3)$ and $(0,1)$ .

1. undefined
2. $y=3$
3. $y+3=0$
4. $0$

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

$y- color(royalblue)(-3)$	$=$	$color(tomato)((-1))(x- color(royalblue)((4)))$	Plug in the values

$y+3$	$=$	$-x + 4$

$-y-3$		$x – 4$	Divide both sides by $-1$
$-y-3 color(crimson)(+y+3)$	$=$	$x – 4 color(crimson)(+y+3)$	Add $y+3$ to both sides
$0$	$=$	$x + y -1$	Simplify
$x + y -1$	$=$	$0$

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

$y- color(royalblue)(5)$	$=$	$color(tomato)((-2))(x- color(royalblue)((3)))$	Plug in the values

$y-5$	$=$	$-2x + 6$

$-y+5$	$=$	$2x – 6$	Multiply both sides by $-1$
$-y+5 color(crimson)(+y-5)$	$=$	$2x – 6 + color(crimson)(+y-5)$	Add $+y-5$ to both sides
$0$	$=$	$2x+y-11$	Simplify
$2x+y-11$	$=$	$0$

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

$y- color(royalblue)(-2)$	$=$	$color(tomato)((0))(x- color(royalblue)((4)))$	Plug in the values

$y+2$	$=$	$0$

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

$(y-color(darkviolet)(-3))/(x-color(forestgreen)(0))$	$=$	$(color(darkviolet)(1)-color(darkviolet)(-3))/(color(forestgreen)(0)-color(forestgreen)(0))$	Plug in the values

$(y-3)/(x)$	$=$	$4/0$



$(y-3)/x$	$=$	$4/0$	Since there is a ‘0’ in the denominator, then the equation is unknown.

Point Slope Form 1

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Quiz summary

Information

1. Question

Hint

Great Work!

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

2. Question

Keep Going!

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

3. Question

Keep Going!

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

4. Question

Keep Going!

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

5. Question

Hint

Fantastic!

Two Point Formula

6. Question

Hint

Excellent!

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

Gradient Formula

7. Question

Keep Going!

Two Point Formula

8. Question

Keep Going!

Two Point Formula

Quizzes

Point Slope Form 1

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Quiz summary

Information

1. Question

Hint

Great Work!

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

2. Question

Keep Going!

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

3. Question

Keep Going!

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

4. Question

Keep Going!

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

5. Question

Hint

Fantastic!

Two Point Formula

6. Question

Hint

Excellent!

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

Gradient Formula

7. Question

Keep Going!

Two Point Formula

8. Question

Keep Going!

Two Point Formula

Quizzes

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

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

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