Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Nov 10, 2023

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

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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