U3: Points on a Line

Front

What is a point on a line?

Back

A point on a line is a specific location defined by its coordinates (x, y) that satisfies the equation of the line.

Front

How do you determine if a point lies on a line given by an equation?

Back

Substitute the x-coordinate of the point into the equation and check if the resulting y-value matches the y-coordinate of the point.

Front

What does the equation y = mx + b represent?

Back

This is the slope-intercept form of a linear equation, where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line measures its steepness and is calculated as the change in y divided by the change in x (rise/run).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

Given the equation y = 2x + 1, what is the y-coordinate when x = 5?

Back

y = 2(5) + 1 = 11.

Front

What is the equation of a line with a slope of 3 and a y-intercept of -2?

Back

The equation is y = 3x - 2.

Front

If a line has a slope of 0, what does that indicate about the line?

Back

A slope of 0 indicates a horizontal line, meaning the y-value remains constant regardless of x.

Front

What is the significance of the coordinates (0, b) in a linear equation?

Back

These coordinates represent the y-intercept of the line.

Front

How do you find the x-coordinate when given a y-coordinate in a linear equation?

Back

Rearrange the equation to solve for x by substituting the given y-value.