5.3 slope intercept form:

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5.3 Slope Intercept Form: Linear Parent Function: is y = x or f(x) = x. Parent Graph: Simplest function of a family of functions with common characteristics. Linear Equation: is an equation that models a linear function. Y-intercept: The point where the graph crosses the y-axis.

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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. GOAL:. - PowerPoint PPT Presentation

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Page 1: 5.3 Slope Intercept Form:

5.3 Slope Intercept Form:

Linear Parent Function: is y = x or f(x) = x.

Parent Graph: Simplest function of a family of functions with common characteristics.

Linear Equation: is an equation that models a linear function.

Y-intercept: The point where the graph crosses the y-axis.

Page 2: 5.3 Slope Intercept Form:

GOAL:

Page 3: 5.3 Slope Intercept Form:

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:

Slope = =

y = m x + b

y-intercepty crossing

Page 4: 5.3 Slope Intercept Form:

EX: Provide the equation of the line in slope-intercept form.?

Page 5: 5.3 Slope Intercept Form:

Solution:The equation must be in slope-intercept form, that is in Y = mx + b1. Find the y-intercept (b) In this graph b = + 5.

2. Find another point to get the slope.

A(0,5)

B(3,8)

A(0,5) B(3,8)

Page 6: 5.3 Slope Intercept Form:

Use the equation of slope to find the slope:

= = = 1

The slope-intercept form equation is:

y = 1x + 5A(0,5)

B(3,8)

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.

Page 7: 5.3 Slope Intercept Form:

When work does not need to be shown: (EOC Test)

A(0,5)

B(3,8)

look at the triangle made by the two points.Count the number of square going up or down and to the right.In this case 3 up and 3 right. Thus slope is 3/3 = 1

Page 8: 5.3 Slope Intercept Form:

YOU TRY IT: Provide the equation of the line in

slope-intercept form.

Page 9: 5.3 Slope Intercept Form:

YOU TRY IT: (Solution)The equation must be in slope-intercept form, that is in Y = mx + b

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)

A(0,4)

B(2,0)

Page 10: 5.3 Slope Intercept Form:

Use the equation of slope to find the slope:

= = = - 2

The slope-intercept form equation is:

y = -2x + 4Remember: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.

A(0,4)

B(2,0)

Page 11: 5.3 Slope Intercept Form:

When no work is required, you can use the rise/run of a right triangle between the two points:

Look at the triangle, down 4 (-4) over to the right 2 (+2) slope = -4/+2 = -2

A(0,4)

B(2,0)

Remember:You MUST KNOW BOTH procedures, the slope formula and the triangle.

Page 12: 5.3 Slope Intercept Form:

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)

Page 13: 5.3 Slope Intercept Form:

Use the given points and equation of slope:

= = = -

We now use the slope and a point to find the y intercept (b).

A(3,-2) B(1,-3)

y = mx + b -3 = - + b

Isolate b: -3 + = b

b = - + = -

Page 14: 5.3 Slope Intercept Form:

Going back to the equation:

y = mx + b

m = - and b = -

To get the final slope-intercept form of the line passing through (3, -2) and(1, -3)

we replace what we have found:

y = - x -

Page 15: 5.3 Slope Intercept Form:

We now proceed to graph the equation:

y = - x - ๐‘น๐’Š๐’”๐’†๐‘น๐’–๐’

Y-intercepty crossing

- 5

2

Page 16: 5.3 Slope Intercept Form:

YOU TRY IT: Write the slope-intercept form of the line that passes through the points (-3, 4) and(2, -1)

Page 17: 5.3 Slope Intercept Form:

Use the given points and equation of slope:

= = = -

We now use the slope and a point to find the y intercept (b).

A(3,-2) B(1,-3)

y = mx + b -3 = - + b

Isolate b: -3 + = b

b = - + = -

Page 18: 5.3 Slope Intercept Form:

Going back to the equation:

y = mx + b

m = - and b = -

To get the final slope-intercept form of the line passing through (3, -2) and(1, -3)

we replace what we have found:

y = - x -

Page 19: 5.3 Slope Intercept Form:

We now proceed to graph the equation:

y = - x - ๐‘น๐’Š๐’”๐’†๐‘น๐’–๐’

Y-intercepty crossing

- 5

2

Page 21: 5.3 Slope Intercept Form:

CLASSWORK:

Page 309-310

Problems: As many as needed to master the concept