Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Equations of motion wikipedia , lookup
Schrödinger equation wikipedia , lookup
Differential equation wikipedia , lookup
Schwarzschild geodesics wikipedia , lookup
Partial differential equation wikipedia , lookup
Exact solutions in general relativity wikipedia , lookup
Dirac equation wikipedia , lookup
Van der Waals equation wikipedia , lookup
Itô diffusion wikipedia , lookup
Derivation of the Navier–Stokes equations wikipedia , lookup
Algebra 1 EOC Summer School Lesson 8: Changes to m and b Introduction to Changing m and b • Remember slope-intercept form of an equation: y = mx + b • m represents the slope • b represents the y-intercept Slope-Intercept Form Example • y=½x–3 • The slope is ½ • The y-intercept is -3 Changing y-intercept • Start with the equation y = ¼ x – 2 • Write the new equation if the y-intercept is increased by 3 units: y = ¼ x + 1 • Graph both lines • How do the lines compare? Describing the effects of changing “b” • What happens to the slope? nothing • What happens to the y-intercept? increases • What happens to the x-intercept? decreases • Describe the relationship between the 2 lines. parallel Changing Slope ¼ times 2 = ½ • Start with the equation y = ¼ x – 2 • Write the new equation if the slope is y=½x–2 doubled: • Graph both lines • How do the lines compare? Describing the effects of changing “m” • What happens to the slope? steeper • What happens to the y-intercept? nothing • What happens to the x-intercept? decreases • Describe the relationship between the 2 lines. intersecting 3 things about slope… 1. Parallel Lines always have the same slope Ex: y = 2x – 5 and y = 2x + 3 2. Perpendicular lines have opposite reciprocal slopes Ex: y = 2x – 3 and y=-½x+4 3. Intersecting lines have slopes that are not the same, but are not opposite reciprocal Ex: y = 3x – 1 and y = 1/3x + 6 Changing m and b • The graph of y = -2x + 1 is graphed below. What is the effect of halving the slope and decreasing the y-intercept by 4 units? Write the new equation: y = -2x + 1 y = -1x – 3 Graph the new line: Describe the Changes • What happens to the slope? Less steep • What happens to the y-intercept? decreased • What happens to the x-intercept? decreases • Describe the relationship between the 2 lines. intersecting