QuestionFind the equation of line $AB$ that passes through points $A(0,-4)$ and $B(6,2)$ . Options are: $y-4=3x$ , $y-2=3(x-6)$ , $y+4=x$ , $y+6=x-2$ .

Studdy Solution

STEP 1

Assumptions1. The line AB passes through the points A(0,-4) and B(6,) . The equation of a line in slope-intercept form is given by $y = mx + c$ , where m is the slope and c is the y-intercept

STEP 2

First, we need to find the slope of the line AB. The slope of a line passing through two points $(x1, y1)$ and $(x2, y2)$ is given by the formula $m = \frac{y2 - y1}{x2 - x1}$

STEP 3

Now, plug in the given values for the points A and B into the slope formula to calculate the slope.
$m = \frac{2 - (-)}{6 -0}$

STEP 4

Calculate the slope.
$m = \frac{2 +4}{6} = \frac{6}{6} =1$

STEP 5

Now that we have the slope, we can find the y-intercept of the line. Since the line passes through the point A(0,-4), the y-intercept is -4.

STEP 6

With the slope and y-intercept, we can write the equation of the line in slope-intercept form.
$y = mx + c$

STEP 7

Plug in the values for the slope and y-intercept into the equation.
$y =1x -4$

STEP 8

implify the equation.
$y = x -4$ So, the equation of the line AB is $y = x -4$ . This is not an option in the given choices. Let's check if any of the given options can be simplified to this form.

STEP 9

The first option is $y -4 =3x$ . If we rearrange this equation to the form $y = mx + c$ , we get $y =3x +4$ . This is not the same as our calculated equation.

STEP 10

The second option is $y -2 =3(x -6)$ . If we simplify this equation, we get $y =3x -16$ . This is not the same as our calculated equation.

STEP 11

The third option is $y +4 = x$ . If we rearrange this equation to the form $y = mx + c$ , we get $y = x -4$ . This is the same as our calculated equation.

STEP 12

The fourth option is $y +6 = x -2$ . If we rearrange this equation to the form $y = mx + c$ , we get $y = x -8$ . This is not the same as our calculated equation.
So, the equation that represents line AB is $y +4 = x$ .

Was this helpful?

QuestionFind the equation of line $AB$ that passes through points $A(0,-4)$ and $B(6,2)$ . Options are: $y-4=3x$ , $y-2=3(x-6)$ , $y+4=x$ , $y+6=x-2$ .

Studdy Solution

STEP 1

Assumptions1. The line AB passes through the points A(0,-4) and B(6,) . The equation of a line in slope-intercept form is given by $y = mx + c$ , where m is the slope and c is the y-intercept

STEP 2

First, we need to find the slope of the line AB. The slope of a line passing through two points $(x1, y1)$ and $(x2, y2)$ is given by the formula $m = \frac{y2 - y1}{x2 - x1}$

STEP 3

Now, plug in the given values for the points A and B into the slope formula to calculate the slope.
$m = \frac{2 - (-)}{6 -0}$

STEP 4

Calculate the slope.
$m = \frac{2 +4}{6} = \frac{6}{6} =1$

STEP 5

Now that we have the slope, we can find the y-intercept of the line. Since the line passes through the point A(0,-4), the y-intercept is -4.

STEP 6

With the slope and y-intercept, we can write the equation of the line in slope-intercept form.
$y = mx + c$

STEP 7

Plug in the values for the slope and y-intercept into the equation.
$y =1x -4$

STEP 8

implify the equation.
$y = x -4$ So, the equation of the line AB is $y = x -4$ . This is not an option in the given choices. Let's check if any of the given options can be simplified to this form.

STEP 9

The first option is $y -4 =3x$ . If we rearrange this equation to the form $y = mx + c$ , we get $y =3x +4$ . This is not the same as our calculated equation.

STEP 10

The second option is $y -2 =3(x -6)$ . If we simplify this equation, we get $y =3x -16$ . This is not the same as our calculated equation.

STEP 11

The third option is $y +4 = x$ . If we rearrange this equation to the form $y = mx + c$ , we get $y = x -4$ . This is the same as our calculated equation.

STEP 12

The fourth option is $y +6 = x -2$ . If we rearrange this equation to the form $y = mx + c$ , we get $y = x -8$ . This is not the same as our calculated equation.
So, the equation that represents line AB is $y +4 = x$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the equation of line ABABAB that passes through points A(0,−4)A(0,-4)A(0,−4) and B(6,2)B(6,2)B(6,2). Options are: y−4=3xy-4=3xy−4=3x, y−2=3(x−6)y-2=3(x-6)y−2=3(x−6), y+4=xy+4=xy+4=x, y+6=x−2y+6=x-2y+6=x−2.

Studdy Solution

STEP 1

Assumptions1. The line AB passes through the points A(0,-4) and B(6,) . The equation of a line in slope-intercept form is given by y=mx+cy = mx + cy=mx+c, where m is the slope and c is the y-intercept

STEP 2

First, we need to find the slope of the line AB. The slope of a line passing through two points (x1,y1)(x1, y1)(x1,y1) and (x2,y2)(x2, y2)(x2,y2) is given by the formulam=y2−y1x2−x1m = \frac{y2 - y1}{x2 - x1}m=x2−x1y2−y1​

STEP 3

Now, plug in the given values for the points A and B into the slope formula to calculate the slope.m=2−(−)6−0m = \frac{2 - (-)}{6 -0}m=6−02−(−)​

STEP 4

Calculate the slope.m=2+46=66=1m = \frac{2 +4}{6} = \frac{6}{6} =1m=62+4​=66​=1

STEP 5

Now that we have the slope, we can find the y-intercept of the line. Since the line passes through the point A(0,-4), the y-intercept is -4.

STEP 6

With the slope and y-intercept, we can write the equation of the line in slope-intercept form.y=mx+cy = mx + cy=mx+c

STEP 7

Plug in the values for the slope and y-intercept into the equation.y=1x−4y =1x -4y=1x−4

STEP 8

implify the equation.y=x−4y = x -4y=x−4So, the equation of the line AB is y=x−4y = x -4y=x−4. This is not an option in the given choices. Let's check if any of the given options can be simplified to this form.

STEP 9

The first option is y−4=3xy -4 =3xy−4=3x. If we rearrange this equation to the form y=mx+cy = mx + cy=mx+c, we get y=3x+4y =3x +4y=3x+4. This is not the same as our calculated equation.

STEP 10

The second option is y−2=3(x−6)y -2 =3(x -6)y−2=3(x−6). If we simplify this equation, we get y=3x−16y =3x -16y=3x−16. This is not the same as our calculated equation.

STEP 11

The third option is y+4=xy +4 = xy+4=x. If we rearrange this equation to the form y=mx+cy = mx + cy=mx+c, we get y=x−4y = x -4y=x−4. This is the same as our calculated equation.

STEP 12

The fourth option is y+6=x−2y +6 = x -2y+6=x−2. If we rearrange this equation to the form y=mx+cy = mx + cy=mx+c, we get y=x−8y = x -8y=x−8. This is not the same as our calculated equation.So, the equation that represents line AB is y+4=xy +4 = xy+4=x.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the equation of line $AB$ that passes through points $A(0,-4)$ and $B(6,2)$ . Options are: $y-4=3x$ , $y-2=3(x-6)$ , $y+4=x$ , $y+6=x-2$ .

Assumptions1. The line AB passes through the points A(0,-4) and B(6,) . The equation of a line in slope-intercept form is given by $y = mx + c$ , where m is the slope and c is the y-intercept

First, we need to find the slope of the line AB. The slope of a line passing through two points $(x1, y1)$ and $(x2, y2)$ is given by the formula $m = \frac{y2 - y1}{x2 - x1}$

Now, plug in the given values for the points A and B into the slope formula to calculate the slope.
$m = \frac{2 - (-)}{6 -0}$

Calculate the slope.
$m = \frac{2 +4}{6} = \frac{6}{6} =1$

With the slope and y-intercept, we can write the equation of the line in slope-intercept form.
$y = mx + c$

Plug in the values for the slope and y-intercept into the equation.
$y =1x -4$

implify the equation.
$y = x -4$ So, the equation of the line AB is $y = x -4$ . This is not an option in the given choices. Let's check if any of the given options can be simplified to this form.

The first option is $y -4 =3x$ . If we rearrange this equation to the form $y = mx + c$ , we get $y =3x +4$ . This is not the same as our calculated equation.

The second option is $y -2 =3(x -6)$ . If we simplify this equation, we get $y =3x -16$ . This is not the same as our calculated equation.

The third option is $y +4 = x$ . If we rearrange this equation to the form $y = mx + c$ , we get $y = x -4$ . This is the same as our calculated equation.

The fourth option is $y +6 = x -2$ . If we rearrange this equation to the form $y = mx + c$ , we get $y = x -8$ . This is not the same as our calculated equation.
So, the equation that represents line AB is $y +4 = x$ .