3.10 Point-Slope, y-intercept, Linear and Exponential

Front

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

Back

The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

How do you convert a linear equation from slope-intercept form to point-slope form?

Back

To convert from slope-intercept form (y = mx + b) to point-slope form (y - y1 = m(x - x1)), identify a point (x1, y1) on the line using the y-intercept (0, b) or any other point.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run). It is often represented by the letter m.

Front

How do you find the y-intercept of a linear equation?

Back

The y-intercept of a linear equation in the form y = mx + b is the value of b, which is the point where the line crosses the y-axis (x=0).

Front

What does it mean for a function to be exponential?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent.

Front

How do you identify the y-intercept from an exponential function?

Back

In an exponential function of the form f(x) = a * b^x, the y-intercept is the value of f(0), which equals a.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

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

Back

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

Front

What is the significance of the slope in real-world applications?

Back

The slope represents the rate of change in real-world applications, such as speed, growth rates, or cost per unit.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts.