Math / Algebra

Question5 Which of the following functions is not a linear function? (a) $y=-\frac{2}{3} x+\frac{11}{2}$ (b) $y=\frac{3-4 x}{7}$ c. $y=\frac{7}{3-4 x}$ d $y=3-x$

Studdy Solution

STEP 1

1. A linear function is of the form $y = mx + b$ , where $m$ and $b$ are constants, and $x$ is the variable.
2. A linear function graphically represents a straight line.
3. A function that is not linear will not fit the form $y = mx + b$ .

STEP 2

1. Analyze each function to determine if it fits the linear form $y = mx + b$ .
2. Identify which function does not fit this form.

STEP 3

Analyze function (a) $y = -\frac{2}{3}x + \frac{11}{2}$ :
This function is in the form $y = mx + b$ where $m = -\frac{2}{3}$ and $b = \frac{11}{2}$ . Therefore, it is a linear function.

STEP 4

Analyze function (b) $y = \frac{3 - 4x}{7}$ :
This can be rewritten as:
$y = \frac{3}{7} - \frac{4}{7}x$
This is in the form $y = mx + b$ where $m = -\frac{4}{7}$ and $b = \frac{3}{7}$ . Therefore, it is a linear function.

STEP 5

Analyze function (c) $y = \frac{7}{3 - 4x}$ :
This function cannot be rewritten in the form $y = mx + b$ because it involves division by an expression containing $x$ . This indicates a non-linear relationship.

STEP 6

Analyze function (d) $y = 3 - x$ :
This function is in the form $y = mx + b$ where $m = -1$ and $b = 3$ . Therefore, it is a linear function.

STEP 7

Identify which function is not linear:
From the analysis, function (c) $y = \frac{7}{3 - 4x}$ does not fit the form $y = mx + b$ and is therefore not a linear function.
The function that is not a linear function is $\boxed{c}$ .

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Question5 Which of the following functions is not a linear function? (a) $y=-\frac{2}{3} x+\frac{11}{2}$ (b) $y=\frac{3-4 x}{7}$ c. $y=\frac{7}{3-4 x}$ d $y=3-x$

Studdy Solution

STEP 1

1. A linear function is of the form $y = mx + b$ , where $m$ and $b$ are constants, and $x$ is the variable.
2. A linear function graphically represents a straight line.
3. A function that is not linear will not fit the form $y = mx + b$ .

STEP 2

1. Analyze each function to determine if it fits the linear form $y = mx + b$ .
2. Identify which function does not fit this form.

STEP 3

Analyze function (a) $y = -\frac{2}{3}x + \frac{11}{2}$ :
This function is in the form $y = mx + b$ where $m = -\frac{2}{3}$ and $b = \frac{11}{2}$ . Therefore, it is a linear function.

STEP 4

Analyze function (b) $y = \frac{3 - 4x}{7}$ :
This can be rewritten as:
$y = \frac{3}{7} - \frac{4}{7}x$
This is in the form $y = mx + b$ where $m = -\frac{4}{7}$ and $b = \frac{3}{7}$ . Therefore, it is a linear function.

STEP 5

Analyze function (c) $y = \frac{7}{3 - 4x}$ :
This function cannot be rewritten in the form $y = mx + b$ because it involves division by an expression containing $x$ . This indicates a non-linear relationship.

STEP 6

Analyze function (d) $y = 3 - x$ :
This function is in the form $y = mx + b$ where $m = -1$ and $b = 3$ . Therefore, it is a linear function.

STEP 7

Identify which function is not linear:
From the analysis, function (c) $y = \frac{7}{3 - 4x}$ does not fit the form $y = mx + b$ and is therefore not a linear function.
The function that is not a linear function is $\boxed{c}$ .

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Question5 Which of the following functions is not a linear function? (a) y=−23x+112y=-\frac{2}{3} x+\frac{11}{2}y=−32​x+211​ (b) y=3−4x7y=\frac{3-4 x}{7}y=73−4x​ c. y=73−4xy=\frac{7}{3-4 x}y=3−4x7​ d y=3−xy=3-xy=3−x

Studdy Solution

STEP 1

1. A linear function is of the form y=mx+b y = mx + b y=mx+b, where m m m and b b b are constants, and x x x is the variable.2. A linear function graphically represents a straight line.3. A function that is not linear will not fit the form y=mx+b y = mx + b y=mx+b.

STEP 2

1. Analyze each function to determine if it fits the linear form y=mx+b y = mx + b y=mx+b.2. Identify which function does not fit this form.

STEP 3

Analyze function (a) y=−23x+112 y = -\frac{2}{3}x + \frac{11}{2} y=−32​x+211​:This function is in the form y=mx+b y = mx + b y=mx+b where m=−23 m = -\frac{2}{3} m=−32​ and b=112 b = \frac{11}{2} b=211​. Therefore, it is a linear function.

STEP 4

STEP 5

Analyze function (c) y=73−4x y = \frac{7}{3 - 4x} y=3−4x7​:This function cannot be rewritten in the form y=mx+b y = mx + b y=mx+b because it involves division by an expression containing x x x. This indicates a non-linear relationship.

STEP 6

Analyze function (d) y=3−x y = 3 - x y=3−x:This function is in the form y=mx+b y = mx + b y=mx+b where m=−1 m = -1 m=−1 and b=3 b = 3 b=3. Therefore, it is a linear function.

STEP 7

Identify which function is not linear:From the analysis, function (c) y=73−4x y = \frac{7}{3 - 4x} y=3−4x7​ does not fit the form y=mx+b y = mx + b y=mx+b and is therefore not a linear function. The function that is not a linear function is c \boxed{c} c​.

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Question5 Which of the following functions is not a linear function? (a) $y=-\frac{2}{3} x+\frac{11}{2}$ (b) $y=\frac{3-4 x}{7}$ c. $y=\frac{7}{3-4 x}$ d $y=3-x$

1. A linear function is of the form $y = mx + b$ , where $m$ and $b$ are constants, and $x$ is the variable.
2. A linear function graphically represents a straight line.
3. A function that is not linear will not fit the form $y = mx + b$ .

1. Analyze each function to determine if it fits the linear form $y = mx + b$ .
2. Identify which function does not fit this form.

Analyze function (a) $y = -\frac{2}{3}x + \frac{11}{2}$ :
This function is in the form $y = mx + b$ where $m = -\frac{2}{3}$ and $b = \frac{11}{2}$ . Therefore, it is a linear function.

Analyze function (c) $y = \frac{7}{3 - 4x}$ :
This function cannot be rewritten in the form $y = mx + b$ because it involves division by an expression containing $x$ . This indicates a non-linear relationship.

Analyze function (d) $y = 3 - x$ :
This function is in the form $y = mx + b$ where $m = -1$ and $b = 3$ . Therefore, it is a linear function.

Identify which function is not linear:
From the analysis, function (c) $y = \frac{7}{3 - 4x}$ does not fit the form $y = mx + b$ and is therefore not a linear function.
The function that is not a linear function is $\boxed{c}$ .