Math / Algebra

Question4. Given the line whose equation is $2 y-6 x=10$ , for every one unit of increase in $x$ , which of the following is true about $y$ ? (Hint, rearrange into $y=m x+b$ form first.) (1) $y$ decreases by 6 (2) $y$ increases by 3 (3) $y$ increases by 2 (4) $y$ decreases by 10

Studdy Solution

STEP 1

1. The line equation given is $2y - 6x = 10$ .
2. We need to rearrange the equation into the slope-intercept form, $y = mx + b$ , where $m$ is the slope.
3. The slope $m$ indicates the change in $y$ for a one-unit increase in $x$ .

STEP 2

1. Rearrange the equation into the slope-intercept form.
2. Identify the slope $m$ .
3. Determine the change in $y$ for a one-unit increase in $x$ .

STEP 3

Rearrange the equation $2y - 6x = 10$ into the slope-intercept form $y = mx + b$ .
Start by isolating $y$ :
$2y = 6x + 10$
Divide every term by 2 to solve for $y$ :
$y = 3x + 5$

STEP 4

Identify the slope $m$ from the equation $y = 3x + 5$ .
The slope $m$ is the coefficient of $x$ , which is 3.

STEP 5

Determine the change in $y$ for a one-unit increase in $x$ .
Since the slope $m = 3$ , for every one unit increase in $x$ , $y$ increases by 3.
The correct statement is: $y$ increases by 3. Therefore, the answer is option (2).

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Question4. Given the line whose equation is $2 y-6 x=10$ , for every one unit of increase in $x$ , which of the following is true about $y$ ? (Hint, rearrange into $y=m x+b$ form first.) (1) $y$ decreases by 6 (2) $y$ increases by 3 (3) $y$ increases by 2 (4) $y$ decreases by 10

Studdy Solution

STEP 1

1. The line equation given is $2y - 6x = 10$ .
2. We need to rearrange the equation into the slope-intercept form, $y = mx + b$ , where $m$ is the slope.
3. The slope $m$ indicates the change in $y$ for a one-unit increase in $x$ .

STEP 2

1. Rearrange the equation into the slope-intercept form.
2. Identify the slope $m$ .
3. Determine the change in $y$ for a one-unit increase in $x$ .

STEP 3

Rearrange the equation $2y - 6x = 10$ into the slope-intercept form $y = mx + b$ .
Start by isolating $y$ :
$2y = 6x + 10$
Divide every term by 2 to solve for $y$ :
$y = 3x + 5$

STEP 4

Identify the slope $m$ from the equation $y = 3x + 5$ .
The slope $m$ is the coefficient of $x$ , which is 3.

STEP 5

Determine the change in $y$ for a one-unit increase in $x$ .
Since the slope $m = 3$ , for every one unit increase in $x$ , $y$ increases by 3.
The correct statement is: $y$ increases by 3. Therefore, the answer is option (2).

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Studdy Solution

STEP 1

1. The line equation given is 2y−6x=102y - 6x = 102y−6x=10.2. We need to rearrange the equation into the slope-intercept form, y=mx+by = mx + by=mx+b, where mmm is the slope.3. The slope mmm indicates the change in yyy for a one-unit increase in xxx.

STEP 2

1. Rearrange the equation into the slope-intercept form.2. Identify the slope mmm.3. Determine the change in yyy for a one-unit increase in xxx.

STEP 3

Rearrange the equation 2y−6x=102y - 6x = 102y−6x=10 into the slope-intercept form y=mx+by = mx + by=mx+b.Start by isolating yyy:2y=6x+10 2y = 6x + 10 2y=6x+10Divide every term by 2 to solve for yyy:y=3x+5 y = 3x + 5 y=3x+5

STEP 4

Identify the slope mmm from the equation y=3x+5y = 3x + 5y=3x+5.The slope mmm is the coefficient of xxx, which is 3.

STEP 5

Determine the change in yyy for a one-unit increase in xxx.Since the slope m=3m = 3m=3, for every one unit increase in xxx, yyy increases by 3. The correct statement is: yyy increases by 3. Therefore, the answer is option (2).

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1. The line equation given is $2y - 6x = 10$ .
2. We need to rearrange the equation into the slope-intercept form, $y = mx + b$ , where $m$ is the slope.
3. The slope $m$ indicates the change in $y$ for a one-unit increase in $x$ .

1. Rearrange the equation into the slope-intercept form.
2. Identify the slope $m$ .
3. Determine the change in $y$ for a one-unit increase in $x$ .

Rearrange the equation $2y - 6x = 10$ into the slope-intercept form $y = mx + b$ .
Start by isolating $y$ :
$2y = 6x + 10$
Divide every term by 2 to solve for $y$ :
$y = 3x + 5$

Identify the slope $m$ from the equation $y = 3x + 5$ .
The slope $m$ is the coefficient of $x$ , which is 3.

Determine the change in $y$ for a one-unit increase in $x$ .
Since the slope $m = 3$ , for every one unit increase in $x$ , $y$ increases by 3.
The correct statement is: $y$ increases by 3. Therefore, the answer is option (2).