Algebra 1 --- Comprehensive Semester 1 Review

Front

What is the slope of a line?

Back

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

Front

How do you find 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 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

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 the y-intercept represent 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

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a(b^x), where a is a constant, b is the base, and x is the exponent.

Front

How do you identify an exponential function from a table of values?

Back

Look for a constant ratio between consecutive y-values as x increases by 1. If the ratio is constant, it indicates an exponential function.

Front

What is the general form of an exponential growth function?

Back

The general form is y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to faster growth over time.

Front

How do you graph a linear equation?

Back

To graph a linear equation, find the y-intercept (b) and plot it on the y-axis, then use the slope (m) to find another point and draw a straight line through both points.