Equation of Line Flashcard

Front

What is the vertical line test used for?

Back

The vertical line test is used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph is not a function.

Front

How do you find the slope of a line given two points?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the slope of the line that passes through the points (3,2) and (4,7)?

Back

The slope is 5, calculated as (7 - 2) / (4 - 3).

Front

What is the general form of the equation of a line?

Back

The general form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

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

Front

What does it mean for a mapping to be a function?

Back

A mapping is a function if each input (x-value) is associated with exactly one output (y-value).

Front

What is the equation of the line that has a slope of -1 and passes through the point (2, 3)?

Back

The equation is y = -x + 5.

Front

What is the significance of the y-intercept in the equation of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

How can you determine if a set of points forms a function?

Back

You can determine if a set of points forms a function by checking if any x-value is repeated with different y-values.

Front

What is the slope of a line that is horizontal?

Back

The slope of a horizontal line is 0.