Question

How to find the slope of an equation with x and y?

a) Identify the coefficient of x in the equation.
b) Take the derivative of the equation with respect to x.
c) Solve the equation for y to obtain the slope.
d) Compare the coefficients of x and y in the equation.

Answer 1

The slope of a linear equation like
`y = a + bx` can be found by identifying the coefficient of x, referred to as b or m. This coefficient represents the slope, and the constant term a or b is the y-intercept.

Step-by-step explanation:

How to Find the Slope of an Equation with x and y:

When looking at the standard form of a linear equation, namely

`y = a + bx`, finding the slope is straightforward. The notation might vary, with some references using
`y = mx + b` instead, but the concept remains unchanged. The coefficient of x, represented by b or m is the slope of the equation. The constant term represented by a or b is the y-intercept.

To find the slope, identify the coefficient of x which is the number multiplying x in the equation. For example, if an equation is given as

`y = 4x + 3`, the slope (m) would be 4. This means for every one unit increase in x, y increases by 4 units. The y-intercept would be 3 indicating where the line crosses the y-axis. Remember, the slope is constant for a straight line, meaning it does not change at any point along the line. Therefore the correct answer to the original question is: a) Identify the coefficient of x in the equation. This is the slope in the context of a linear equation with variables x and y.