Chapter+5

Change. (y2 - y1)/(x2 - x1). Another thing for slope is m. Slope can be: Positive if the line goes up. Negative if the line goes down. Zero if the line is horizontal. Undefined if the line is vertical. Rate of change tells on average how a quantity changes over time. It can change in quantity/change over time. At least need 2 points of data needed in order to work with. (2, 3) and (7, 10). (y2 - y1)/(x2 - x1) is the formula for slope. So (10 - 3)/(7 - 2). Subtract and you get, 7/5 or 1/2/5. Remember, it is okay to leave the slope as an improper fraction, you don't have to, but you can. Steps to find a missing point or value: (r, 6) (7, 10). Slope is 1/2. Do slope formula. 1/2(10 - 6)/(7 - r). You have to cross multiply. 2(10 - 6) = 1(7 - r). Distribute. 20 - 12 = 7 -r. 8 = 7 - r. 7 + 1 = 8. r = 1. Vocab: Direct variation- Constant of variation- (k) Family of graphs- Graphs and equations of graphs that have common characteristics. Common difference in your table is your slope. Parent graphs- When you find the opposite reciprocal you have a perpendicular line. //Linear Extrapolation -// Based on info, predict where the data is going like what pattern or somewhat. //Absolute Value Function -// f(x) = 14 //Classes of Functions -//
 * //5.1- Find the slope of a line. Use rate of change to solve problems.//**
 * Notes:** Slope is the ratio of the y coordinate to corresponding x coordinate. It goes by rise/run. How fast the line goes up and down. The change of y/ the change of x. It is determined by x and y coordinates of 2 points. (*y/*x) *
 * //5.2- Write and graph direct variation equations. Solve problems using direct variation.//**
 * Notes:** Direct variation is when 2 variables are related so the ratio of the values is always the same. Also, the relationship of the 2 variables where 1 is a constant multiple of the other. Or if "a" is always 2 * b then they directly vary. Definition: x is always multiplied by the same number, (k) to get the y value. Direct variation equations will always go through (0, 0) because nothing is being added or subtracted. Instead of y = mx + b, our slope (m) our slope is now shown through k. y = kx, k cannot = 0. y varies directly with x, k tells us how much.
 * //5.3- Write and graph linear equations in slope-intercept form. Model real world data with an equation in slope-intercept form.//**
 * Notes:** Y = mx + b. M is the slope. B is y intercept. You can use 2 points to find slope intercept form. Common difference is slope (m). Y intercept is the point where the line crosses the y axis.
 * //5.4- Write an equation of s line given the slope and one point on the line. Write an equation of a line given two points on a line.//**
 * Notes:** Y = mx + b. Steps: **1.)** Plug in numbers that you know. **2.)** Solve for b. **3.)** Rewrite equation, and substitute only m & b.
 * //5.6- Write an equation that passes through a given point parallel to a given line.Write an equation of the line that passes through a given point, perpendicular to a given line.//**
 * Notes:** Two lines are parallel if they never cross and their slopes are the same. Two lines are perpendicular if they create a right angle and their slopes are opposite reciprocal//**.**// You know an equation is parallel if it the slope stays the same, but the y intercept changes to any number. You know an equation is perpendicular if it the slope changes and has an opposite reciprocal of the slope.
 * //5.7- Be able to interpret scatter plots. Create a line of fit for scatter plots.//**
 * Notes:** #20 is +. Scatter plot summary written as a slope.

y - y1 = m(x - x1)
 * //__Plug in a zero and solve for x. Plug in a zero for y and solve for x.__//**