Slope and Graphing

Front

What is the definition of slope in a graph?

Back

The slope is the constant rate of change between two points on a line, often represented as 'm' in the slope-intercept form of a linear equation.

Front

How do you determine if a point is a solution to a system of equations?

Back

A point (x,y) is a solution to a system of equations if it satisfies all equations in the system, meaning it makes each equation true when the x and y values are substituted.

Front

What does it mean if a slope is undefined?

Back

An undefined slope occurs in a vertical line where the change in x is zero, leading to division by zero in the slope formula.

Front

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

Back

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

Front

What is the formula to calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant from left to right.

Front

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

Back

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

Front

How can you graph a linear equation using its slope and y-intercept?

Back

To graph a linear equation, start at the y-intercept on the y-axis, then use the slope to determine the rise over run to find another point on the line.

Front

What is the relationship between parallel lines and their slopes?

Back

Parallel lines have the same slope, meaning they never intersect and maintain a constant distance apart.