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## 5.3 Slope Intercept Form:

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Parent Graph: Simplest function of a family of functions**with common characteristics. 5.3 Slope Intercept Form: Linear Parent Function: is y = x or f(x) = x. Linear Equation: is an equation that models a linear function. Y-intercept: The point where the graph crosses the y-axis.**Whenever we are given a graph we must be able to provide the**equation of the function. Slope-Intercept Form: The linear equation of a nonvertical line: y = m x + b Slope = = y-intercepty crossing**EX: Provide the equation of the line in**slope-intercept form.?**Solution:The equation must be in slope-intercept form, that**is in Y = mx + b B(3,8) 1. Find the y-intercept (b) A(0,5) In this graph b = + 5. 2. Find another point to get the slope. A(0,5) B(3,8)**Use the equation of slope to find the slope:**= = = 1 B(3,8) The slope-intercept form equation is:y = 1x + 5 A(0,5) Remember:This means that if you start a 5 and move up one and over to the right one, and continue this pattern, you can get many points ON this line.**When work does not need to be shown: (EOC Test)**look at the triangle made by the two points. B(3,8) A(0,5) Count the number of square going up or down and to the right. In this case 3up and 3 right. Thus slope is 3/3 = 1**YOU TRY IT:Provide the equation of the line in**slope-intercept form.**YOU TRY IT: (Solution)The equation must be in**slope-intercept form, that is in Y = mx + b A(0,4) 1. Find the y-intercept (b) In this graph b = + 4. 2. Find another point to get the slope. A(0,4) B(2,0) B(2,0)**Use the equation of slope to find the slope:**= = = - 2 A(0,4) The slope-intercept form equation is:y = -2x + 4 B(2,0) Remember:This means that if you start a 4 and move down two and over to the right one, and continue this pattern, you can get many points ON this line.**When no work is required, you can use the rise/run of a**right triangle between the two points: A(0,4) Look at the triangle, down 4 (-4) over to the right 2 (+2) slope = -4/+2 = -2 B(2,0) Remember:You MUST KNOW BOTH procedures, the slope formula and the triangle.**Given Two Points: We can also create an equation in the**slope-intercept form from any two points: EX: Write the slope-intercept form of the line that passes through the points (3, -2) and(1, -3)**Use the given points and equation of slope:**B(1,-3) A(3,-2) = = = - We now use the slope and a point to find the y intercept (b). y = mx + b -3 = - + b -3 += b Isolate b: b = - + = -**Going back to the equation:**y = mx + b we replace what we have found: m = - and b = - To get the final slope-intercept form of the line passing through (3, -2) and(1, -3) y = -x -**We now proceed to graph the equation:**y = -x - Y-intercepty crossing - 5 2**YOU TRY IT:Write the slope-intercept form of the line that**passes through the points (-3, 4) and(2, -1)**Use the given points and equation of slope:**B(1,-3) A(3,-2) = = = - We now use the slope and a point to find the y intercept (b). y = mx + b -3 = - + b -3 += b Isolate b: b = - + = -**Going back to the equation:**y = mx + b we replace what we have found: m = - and b = - To get the final slope-intercept form of the line passing through (3, -2) and(1, -3) y = -x -**We now proceed to graph the equation:**y = -x - Y-intercepty crossing - 5 2**CLASSWORK:Page 309-310**Problems: 2, 3, 6, 8, All ODDS .