Solved on Jan 18, 2024

Find the equation of the linear function passing through the point $(x, y) = (-4, 6)$ with slope $2$ .

STEP 1

Assumptions
1. The equation of the linear function is $y-6=2(x+4)$ .
2. We need to find which of the given points lies on the line represented by this equation.

STEP 2

First, we will simplify the equation of the linear function to the slope-intercept form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
$y - 6 = 2(x + 4)$

STEP 3

Distribute the 2 on the right-hand side of the equation.
$y - 6 = 2x + 8$

STEP 4

Add 6 to both sides of the equation to isolate $y$ .
$y = 2x + 8 + 6$

STEP 5

Combine like terms to get the final slope-intercept form of the equation.
$y = 2x + 14$

STEP 6

Now we will test each point to see if it satisfies the equation $y = 2x + 14$ . If a point satisfies the equation, it means the point lies on the line.

STEP 7

Test the point $(-4, 6)$ .
$y = 2x + 14$
$6 = 2(-4) + 14$

STEP 8

Calculate the right-hand side of the equation.
$6 = -8 + 14$

STEP 9

Combine like terms.
$6 = 6$
Since the equation holds true, the point $(-4, 6)$ is on the line.

STEP 10

Test the point $(4, -6)$ .
$y = 2x + 14$
$-6 = 2(4) + 14$

STEP 11

Calculate the right-hand side of the equation.
$-6 = 8 + 14$

STEP 12

Combine like terms.
$-6 = 22$
Since the equation does not hold true, the point $(4, -6)$ is not on the line.

STEP 13

Test the point $(2, -2)$ .
$y = 2x + 14$
$-2 = 2(2) + 14$

STEP 14

Calculate the right-hand side of the equation.
$-2 = 4 + 14$

STEP 15

Combine like terms.
$-2 = 18$
Since the equation does not hold true, the point $(2, -2)$ is not on the line.
The point that is on the line is $(-4, 6)$ .

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Find the equation of the linear function passing through the point $(x, y) = (-4, 6)$ with slope $2$ .

STEP 1

Assumptions
1. The equation of the linear function is $y-6=2(x+4)$ .
2. We need to find which of the given points lies on the line represented by this equation.

STEP 2

First, we will simplify the equation of the linear function to the slope-intercept form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
$y - 6 = 2(x + 4)$

STEP 3

Distribute the 2 on the right-hand side of the equation.
$y - 6 = 2x + 8$

STEP 4

Add 6 to both sides of the equation to isolate $y$ .
$y = 2x + 8 + 6$

STEP 5

Combine like terms to get the final slope-intercept form of the equation.
$y = 2x + 14$

STEP 6

Now we will test each point to see if it satisfies the equation $y = 2x + 14$ . If a point satisfies the equation, it means the point lies on the line.

STEP 7

Test the point $(-4, 6)$ .
$y = 2x + 14$
$6 = 2(-4) + 14$

STEP 8

Calculate the right-hand side of the equation.
$6 = -8 + 14$

STEP 9

Combine like terms.
$6 = 6$
Since the equation holds true, the point $(-4, 6)$ is on the line.

STEP 10

Test the point $(4, -6)$ .
$y = 2x + 14$
$-6 = 2(4) + 14$

STEP 11

Calculate the right-hand side of the equation.
$-6 = 8 + 14$

STEP 12

Combine like terms.
$-6 = 22$
Since the equation does not hold true, the point $(4, -6)$ is not on the line.

STEP 13

Test the point $(2, -2)$ .
$y = 2x + 14$
$-2 = 2(2) + 14$

STEP 14

Calculate the right-hand side of the equation.
$-2 = 4 + 14$

STEP 15

Combine like terms.
$-2 = 18$
Since the equation does not hold true, the point $(2, -2)$ is not on the line.
The point that is on the line is $(-4, 6)$ .

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Find the equation of the linear function passing through the point (x,y)=(−4,6)(x, y) = (-4, 6)(x,y)=(−4,6) with slope 222.

STEP 1

Assumptions1. The equation of the linear function is y−6=2(x+4)y-6=2(x+4)y−6=2(x+4).2. We need to find which of the given points lies on the line represented by this equation.

STEP 2

First, we will simplify the equation of the linear function to the slope-intercept form y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept.y−6=2(x+4)y - 6 = 2(x + 4)y−6=2(x+4)

STEP 3

Distribute the 2 on the right-hand side of the equation.y−6=2x+8y - 6 = 2x + 8y−6=2x+8

STEP 4

Add 6 to both sides of the equation to isolate yyy.y=2x+8+6y = 2x + 8 + 6y=2x+8+6

STEP 5

Combine like terms to get the final slope-intercept form of the equation.y=2x+14y = 2x + 14y=2x+14

STEP 6

Now we will test each point to see if it satisfies the equation y=2x+14y = 2x + 14y=2x+14. If a point satisfies the equation, it means the point lies on the line.

STEP 7

Test the point (−4,6)(-4, 6)(−4,6).y=2x+14y = 2x + 14y=2x+146=2(−4)+146 = 2(-4) + 146=2(−4)+14

STEP 8

Calculate the right-hand side of the equation.6=−8+146 = -8 + 146=−8+14

STEP 9

Combine like terms.6=66 = 66=6Since the equation holds true, the point (−4,6)(-4, 6)(−4,6) is on the line.

STEP 10

Test the point (4,−6)(4, -6)(4,−6).y=2x+14y = 2x + 14y=2x+14−6=2(4)+14-6 = 2(4) + 14−6=2(4)+14

STEP 11

Calculate the right-hand side of the equation.−6=8+14-6 = 8 + 14−6=8+14

STEP 12

Combine like terms.−6=22-6 = 22−6=22Since the equation does not hold true, the point (4,−6)(4, -6)(4,−6) is not on the line.

STEP 13

Test the point (2,−2)(2, -2)(2,−2).y=2x+14y = 2x + 14y=2x+14−2=2(2)+14-2 = 2(2) + 14−2=2(2)+14

STEP 14

Calculate the right-hand side of the equation.−2=4+14-2 = 4 + 14−2=4+14

STEP 15

Combine like terms.−2=18-2 = 18−2=18Since the equation does not hold true, the point (2,−2)(2, -2)(2,−2) is not on the line.The point that is on the line is (−4,6)(-4, 6)(−4,6).

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Find the equation of the linear function passing through the point $(x, y) = (-4, 6)$ with slope $2$ .

Assumptions
1. The equation of the linear function is $y-6=2(x+4)$ .
2. We need to find which of the given points lies on the line represented by this equation.

First, we will simplify the equation of the linear function to the slope-intercept form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
$y - 6 = 2(x + 4)$

Distribute the 2 on the right-hand side of the equation.
$y - 6 = 2x + 8$

Add 6 to both sides of the equation to isolate $y$ .
$y = 2x + 8 + 6$

Combine like terms to get the final slope-intercept form of the equation.
$y = 2x + 14$

Now we will test each point to see if it satisfies the equation $y = 2x + 14$ . If a point satisfies the equation, it means the point lies on the line.

Test the point $(-4, 6)$ .
$y = 2x + 14$
$6 = 2(-4) + 14$

Calculate the right-hand side of the equation.
$6 = -8 + 14$

Combine like terms.
$6 = 6$
Since the equation holds true, the point $(-4, 6)$ is on the line.

Test the point $(4, -6)$ .
$y = 2x + 14$
$-6 = 2(4) + 14$

Calculate the right-hand side of the equation.
$-6 = 8 + 14$

Combine like terms.
$-6 = 22$
Since the equation does not hold true, the point $(4, -6)$ is not on the line.

Test the point $(2, -2)$ .
$y = 2x + 14$
$-2 = 2(2) + 14$

Calculate the right-hand side of the equation.
$-2 = 4 + 14$

Combine like terms.
$-2 = 18$
Since the equation does not hold true, the point $(2, -2)$ is not on the line.
The point that is on the line is $(-4, 6)$ .