Question Determine if the linear equation $y = -2x + 3$ represents a linear function. Explain your reasoning.

Studdy Solution

STEP 1

Assumptions1. The equation given is $y=-x+3$ . We are asked to confirm if the relation is a linear function

STEP 2

A linear function is any function that graphs to a straight line. What this means mathematically is that the function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

STEP 3

The general form of a linear function is $y = mx + c$ , where m is the slope of the line and c is the y-intercept.

STEP 4

Comparing the given equation $y=-2x+3$ with the general form $y = mx + c$ , we can see that the equation represents a straight line with slope -2 and y-intercept3.

STEP 5

Since the given equation fits the general form of a linear function, we can conclude that the relation is indeed a linear function.
So, the relation $y=-2x+3$ is a linear function.

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Question Determine if the linear equation $y = -2x + 3$ represents a linear function. Explain your reasoning.

Studdy Solution

STEP 1

Assumptions1. The equation given is $y=-x+3$ . We are asked to confirm if the relation is a linear function

STEP 2

A linear function is any function that graphs to a straight line. What this means mathematically is that the function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

STEP 3

The general form of a linear function is $y = mx + c$ , where m is the slope of the line and c is the y-intercept.

STEP 4

Comparing the given equation $y=-2x+3$ with the general form $y = mx + c$ , we can see that the equation represents a straight line with slope -2 and y-intercept3.

STEP 5

Since the given equation fits the general form of a linear function, we can conclude that the relation is indeed a linear function.
So, the relation $y=-2x+3$ is a linear function.

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Question Determine if the linear equation y=−2x+3y = -2x + 3y=−2x+3 represents a linear function. Explain your reasoning.

Studdy Solution

STEP 1

Assumptions1. The equation given is y=−x+3y=-x+3y=−x+3 . We are asked to confirm if the relation is a linear function

STEP 2

A linear function is any function that graphs to a straight line. What this means mathematically is that the function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

STEP 3

The general form of a linear function is y=mx+cy = mx + cy=mx+c, where m is the slope of the line and c is the y-intercept.

STEP 4

Comparing the given equation y=−2x+3y=-2x+3y=−2x+3 with the general form y=mx+cy = mx + cy=mx+c, we can see that the equation represents a straight line with slope -2 and y-intercept3.

STEP 5

Since the given equation fits the general form of a linear function, we can conclude that the relation is indeed a linear function.So, the relation y=−2x+3y=-2x+3y=−2x+3 is a linear function.

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Studdy solves anything!

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

Question Determine if the linear equation $y = -2x + 3$ represents a linear function. Explain your reasoning.

Assumptions1. The equation given is $y=-x+3$ . We are asked to confirm if the relation is a linear function

The general form of a linear function is $y = mx + c$ , where m is the slope of the line and c is the y-intercept.

Comparing the given equation $y=-2x+3$ with the general form $y = mx + c$ , we can see that the equation represents a straight line with slope -2 and y-intercept3.

Since the given equation fits the general form of a linear function, we can conclude that the relation is indeed a linear function.
So, the relation $y=-2x+3$ is a linear function.