Question

Explain how to change an Linear Equation from Standard form to slope intercept form. Tell me two reasons that it is important to be able to have the linear equation in slope intercept form.

Answer 1

A) The standard form of a linear equation is given as follows;

Ax + By = C

In order to change the above linear equation from standard form to slope and intercept form which is the form y = mx + c, we have;

1) Move the x-variable (and its coefficient) to the right side of the equation as follows;

By = C - Ax

2) Divide both sides of the equation above equation, by the coefficient of y as follows;

By/B = C/B - Ax/B

y = C/B - A/B·x

3) Rearrange the right hand side of the above equation

y = -A/B·x + C/B

The equation given above is in the slope and intercept form, y = m·x + c, where;

m = -A/B

c = C/B

B) Two reasons why it is important to have a slope and intercept form of a linear equation are;

1) The slope and intercept for shows the initial value of the dependent variable, y, when the dependent variable, x is 0 which is the constant term, c, in the equation

2) The slope coefficient term, m, in the slope and intercept form of a linear equation shows the rate of increase of the y-coordinate value with a unit increase in x-coordinate value.

Explanation: