rewriting Linear Equations

Writing Linear Equations

1. Start with the standard form: Ax + By = C 2. Rearrange the equation to isolate the y variable 3. Divide all terms by the greatest common factor to simplify 4. Use slope-intercept form (y = mx + b) to find the slope and y-intercept 5. Substitute values to find the equation

Isolating the y Variable

Trivia: Rearranging the equation to isolate the y variable helps in finding the slope and y-intercept. It simplifies the equation and allows for easier substitution of values. It is a crucial step in solving linear equations.

Converting Standard Form to Slope-Intercept Form

To convert a linear equation from standard form (Ax + By = C) to slope-intercept form (y = mx + b), follow these steps: 1. Solve for y to isolate it on one side of the equation. 2. Rewrite the equation in the form y = mx + b, where m is the slope and b is the y-intercept. 3. Simplify the equation if necessary. 4. The resulting equation is in slope-intercept form.

Converting Linear Equations

Trivia: Did you know that converting a linear equation from standard form to slope-intercept form helps us easily identify the slope and y-intercept? Here are the steps: 1. Solve for x to isolate it. 2. Rewrite the equation as y = mx + b. 3. Simplify if needed. Now you have the equation in slope-intercept form!

Writing Linear Equations

Learn how to write linear equations in point-slope form. Use the formula y - y1 = m(x - x1) to find the equation of a line given a point and slope. Remember to substitute the values of x1, y1, and m into the equation.

Point-Slope Form

y - y1 = m(x - x1) is the formula used to find the equation of a line in point-slope form. This form is useful for finding the equation of a line when given a point on the line and the slope of the line. It allows us to easily express the equation of a line in a concise and straightforward manner.

Perpendicular Lines:

• Definition: Two lines that intersect at a right angle.
• Equation: The equation of a perpendicular line to y = mx + b is y = -1/mx + c, where c is the y-intercept.
• Example: Find the equation of a line perpendicular to y = 2x + 3.

Perpendicular Line:

Trivia: A line perpendicular to y = 2x + 3 has a slope that is the negative reciprocal of 2, which is -1/2. The equation of the perpendicular line is y = -1/2x + 3. This means that the new line will intersect the original line at a right angle.