Question

Use an algebra calculator to convert the general form to intercept form.

a) Ax + By = C
b) y = mx + b
c) (x - a)(x - b) = 0
d) x²+ y² = r²

Answer 1

Converting equations into intercept form involves using algebra to solve for y in linear equations and for roots in quadratic equations. The slope and y-intercept are key concepts in linear equations, while quadratic equations can be expressed in terms of their roots.

Step-by-step explanation:

Converting various forms of equations into the intercept form can be understood in the context of algebra. Here, we'll focus on understanding the slope and y-intercept of a linear equation and how to express a quadratic equation in terms of its roots.

Linear Equation in Slope-Intercept Form

For a linear equation in the form y = mx + b, m represents the slope and b represents the y-intercept. The slope describes the steepness of the line, and the y-intercept is the y-coordinate of the point where the line crosses the y-axis. Hence, the general form Ax + By = C can be converted to the slope-intercept form by solving for y.

Quadratic Equations

Quadratic equations are of the form ax² + bx + c = 0. To express a quadratic equation in intercept form, which is (x - a)(x - b) = 0, you would solve for the roots of the equation using the quadratic formula, and those roots would be a and b in the intercept form.

Circle Equation

For a circle equation of the form x² + y² = r², this is already in the standard form, and it represents a circle with radius r centered at the origin. Intercept form is not typically used for circle equations.