Presentation on theme: "3.5 Graphing Linear Equations in Slope-Intercept Form"— Presentation transcript: 1 3.5 Graphing Linear Equations in Slope-Intercept Form Show
2 Slope Describes the rate of change between any two points on a line. It is the measure of the steepness of the line Slope =
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥 = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 Slope = 1/2 Slope = 2 4 2 4 3
Slope Describes the rate of change between any two points on a line. It is the measure of the steepness of the line Slope = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥 = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 Slope = m = 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 4 Example 1:
Finding the Slope of a Line
5 Example 1: Finding the Slope of a Line 6 You try! m = 1−3 1−−4 m = 3−−1 3−−3 m = −3−4 2−5 m = −2 5 m = 4 6 7 Example 2: Finding the Slope From a Table 8 Example 2: Finding the Slope From a Table 9
Example 2: Finding the Slope From a Table
10 You try! 4.) The points represented by the table lie on a line What is the slope of the line? x 2 4 6 8
y 10 15 20 25 m = 5 2 11 Using the Slope-Intercept Form of a Linear Equation 12 Example 3: Identifying Slopes and y-Intercepts
13 You try! Find the slope and y-intercept of the graph if the linear equations. 5.) y = -6x ) y = 8 7.) x + 4y = -10
Slope = -6 y-intercept= 1 y = 0x + 8 Slope = 0 y-intercept = 8 x + 4y = -10 -x x 4y = -x – 10 y = −1 4 x – 10 4 y = −1 4 x – Slope= -1/4 y-intercept=
14 Example 4: Using Slope-Intercept Form to Graph
15 Example 5: Graphing from a Verbal Description
16 Example 5: Graphing from a Verbal Description 17 Example 5: Graphing from a Verbal Description 18 Example 5:
Graphing from a Verbal Description
19 You try! Graph the linear equation and identify the x-intercept. 20 You try! 10) A linear function h models a relationship in which the dependent variable
decreases by 2 units for every 5 units the independent variable increases. Graph h when h(0) = 4. Identify the slope, y-intercept and x-intercept of the graph. Slope = −2 5 y-intercept = 4 x-intercept =10 21 Example 6: Solving Real-Life Problems 22 Example 6: Solving Real-Life Problems 23
Example 6: Solving Real-Life Problems 24 You try! 11) The elevation of the submersible is modeled by h(t) = 500t – 10,000. Graph the function and identify its domain and range. Interpret the slope and intercepts of the graph. How do you write an equation in slopeWe can write the slope-intercept equation from a graph. The point where the graph crosses the y-axis is our b-value. The slope is our m-value. Plug these into y=mx+b.
How do you find the slope and yThe slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.
How do you write linear equations?The standard form is ax+by+c=0 a x + b y + c = 0 and its features are the slope, x-intercept, and y-intercept. An example of a linear equation is: 2x + y - 3 = 0. It can be written in the standard form, the slope-intercept form, and the point-slope form.
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