Linear Equations in Two Variables

These flashcards cover key concepts related to linear equations in two variables, including definitions, forms, and problem-solving techniques.

What is a linear equation in two variables?

A first-degree equation whose graph is a line.

What is the slope in relation to a linear equation?

The ratio of rise to run; it determines the steepness of a line.

What is the standard form of a linear equation?

ax + by = c, where a, b, and c are real numbers, and a and b are not equal to zero.

What is the slope-intercept form of a linear equation?

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

How do you identify the x-intercept of a linear equation?

Set y to 0 in the equation and solve for x.

How do you determine the y-intercept of a linear equation?

Set x to 0 in the equation and solve for y.

What does an ordered pair represent in a Cartesian plane?

The location of a point, where the first value is the x-coordinate and the second value is the y-coordinate.

What is the meaning of intercepts in the context of a linear equation?

Points where the graph of a linear equation intersects the axes.

What is the purpose of graphing a linear equation?

To visualize the relationship between the variables x and y.

How is the slope classified in relation to its value?

Positive slope rises from left to right; negative slope falls from left to right; zero slope is a horizontal line; undefined slope is a vertical line.

What is the relationship between the distance traveled (x) and the total cost (y) in a jeepney ride?

The linear equation y = 2x + 13 represents the relationship.

What are the steps to graph a linear equation?

Find the x- and y-intercepts, plot these points, and connect them to form a line.

What does it mean if a pair of coordinates satisfies a linear equation?

It means that the point represented by the coordinates lies on the graph of the equation.

What is a slope of 0 in a graph?

It represents a horizontal line.

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

They dictate the steepness and direction of the line.

In the context of a linear equation, what does 'rise' refer to?

The vertical change between two points on the graph.

What does 'run' refer to in terms of linear equations?

The horizontal change between two points on the graph.

In Activity 2, what is the total cost of the jeepney ride for an additional 10km?

₱33.00.