Does (x, y) satisfy the linear function?

Learning Objectives Define what it means for a point to 'satisfy' a linear function. Accurately substitute given (x, y) coordinates into a linear equation. Evaluate both sides of a linear equation after substitution. Determine if a given point lies on the graph of a linear function by checking for equality. Explain the graphical meaning of a point satisfying a linear function. Identify if a point is a solution to a linear equation. Ever wonder if a specific spot on a map is exactly on a particular road? 🗺️ That's similar to asking if a point (x, y) satisfies a linear function! In this lesson, you'll learn how to check if a specific point, represented by its coordinates (x, y), makes a linear equation true. This skill is fundamental for understanding grap...

TermDefinitionExample Coordinate Pair (x, y)An ordered pair of numbers that specifies the location of a point on a coordinate plane. The first number, x, is the horizontal position, and the second number, y, is the vertical position.The point (3, 2) means 3 units to the right of the origin and 2 units up. Linear Function/EquationAn equation whose graph is a straight line. It describes a relationship where the change in y is proportional to the change in x.y = 2x + 1 or 3x - y = 5 Satisfy (an equation)A point (x, y) 'satisfies' a linear equation if, when its x and y values are substituted into the equation, the equation becomes a true mathematical statement.The point (1, 3) satisfies y = 2x + 1 because 3 = 2(1) + 1 simplifies to 3 = 3, which is true. Solution (to an equation)Any...

The Satisfaction Rule for Linear Functions A point $(x, y)$ satisfies a linear function if, when its coordinates are substituted into the function's equation, the resulting statement is true (i.e., the left side equals the right side). To check if a point is on a line, plug in its x-coordinate for 'x' and its y-coordinate for 'y' into the equation. If both sides of the equation are equal, the point satisfies the function and lies on its graph. Slope-Intercept Form $y = mx + b$ This is a common form for linear equations where 'm' is the slope and 'b' is the y-intercept. You can substitute x and y directly into this form to check for satisfaction. Standard Form $Ax + By = C$ Another common form for linear equations. 'A&...