1A. Linear Functions
Instructions:
- Use the input boxes and slider tools for and to adjust the slope and vertical intercept of the line, respectively.
- Use the input box for to move the point on the line. Use the slider tool for to adjust how far away the second point is from the first point.
- Use the slider tool for and then for to see a visual representation of the slope of the line.
Linear Functions
Slope-Intercept Form: Linear functions have the form , where is the slope of the line and is the vertical intercept.
Slope: The slope between any two points and can be calculated by:
Point-Slope Form: If a point on the line and the slope of the line are both known, then you can write an equation of the line using the slope formula by leaving the coordinates of a second point as variables . By multiplying both sides of the slope formula by the denominator to get rid of the fraction, we obtain the point-slope form of a linear equation: