Algebra 1 Mid-Year Review

Front

What is the definition of a slope in a linear equation?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line, which is calculated as the change in y divided by the change in x (rise over run).

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

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

Front

What does the equation of a line in slope-intercept form look like?

Back

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

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 'b' in the slope-intercept form of the equation.

Front

How do you graph a linear equation?

Back

To graph a linear equation, identify the y-intercept (b), plot it on the y-axis, then use the slope (m) to find another point by moving up/down and left/right from the y-intercept.

Front

What is the difference between a linear equation and an inequality?

Back

A linear equation represents a straight line, while a linear inequality shows a region of the graph that satisfies the inequality, often represented with a dashed or solid line.

Front

What does it mean if a line is increasing?

Back

A line is increasing if the slope is positive, meaning as x increases, y also increases.

Front

What does it mean if a line is decreasing?

Back

A line is decreasing if the slope is negative, meaning as x increases, y decreases.

Front

How do you determine if a point lies above, below, or on a line?

Back

To determine the position of a point relative to a line, substitute the x-value of the point into the line's equation and compare the resulting y-value to the y-value of the point.

Front

What is the significance of a dashed line in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set of the inequality.