What is the slope of the line represented by the equation y = -1/2x + 1/4

Solution:

The slope of a line is the ratio of change in y-coordinates to change in x-coordinates of any two points on the line.

It is denoted by m.

m = Δy / Δx

The slope of a line is also defined as the measure of the tangent of the angle made by the line with the x-axis.

m = tanθ = (y₂ - y₁) / (x₂ - x₁) where (x₁, y₁) and (x₂, y₂) are two points on the line.

Given, the equation y = -1/2x + 1/4 --- (1)

We have to find the slope of the equation.

The equation of the line in slope-intercept form is given by

y = mx + c --- (2)

Where, m is the slope

c is the y-intercept.

Comparing (1) and (2)

m = -1/2.

Therefore, the slope of the equation is -1/2.

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What is the slope of the line represented by the equation y = -1/2x + 1/4

Summary:

The slope of the line represented by the equation y = -1/2x + 1/4 is -1/2.