Writing Equations & Solving Systems

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is slope-intercept form of a linear equation?

Back

The form y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

How do you write the equation of a line given a point and a slope?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients represent the slope and the y-intercept, determining the line's steepness and position.

Front

How can you determine if a point lies on a line given its equation?

Back

Substitute the x-value of the point into the equation and see if the resulting y-value matches the point's y-value.