Ex 1: Write the equation of the graphed line in slope-intercept form.

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Presentation transcript:

Ex 1: Write the equation of the graphed line in slope-intercept form. Step 1 Identify the y-intercept. The y-intercept b is 1. Step 2 Find the slope. Choose any two convenient points on the line, such as (0, 1) and (4, –2). Count from (0, 1) to (4, –2) to find the rise and the run. The rise is –3 units and the run is 4 units. 3 –4 4 –3 Slope is = = – . rise run –3 4 3 Step 3 Write the equation in slope-intercept form. y = mx + b y = – ¾x + 1

Notice that for two points on a line, the rise is the differences in the y-coordinates, and the run is the differences in the x-coordinates. Using this information, we can define the slope of a line by using a formula.

Ex 2: Find the slope of the line through (–1, 1) and (2, –5). Let (x1, y1) be (–1, 1) and (x2, y2) be (2, –5). The slope of the line is –2. Find the slope of the line. x 4 8 12 16 y 2 5 11 Let (x1, y1) be (4, 2) and (x2, y2) be (8, 5). The slope of the line is ¾.

Because the slope of line is constant, it is possible to use any point on a line and the slope of the line to write an equation of the line in point-slope form. Ex 3: In slope-intercept form, write the equation of the line that contains the points in the table. x –8 –4 4 8 y –5 –3.5 –0.5 1 First, find the slope. Let (x1, y1) be (–8, –5) and (x2, y2) be (8, 1). Next, choose a point, and use either form of the equation of a line.

Method A Point-Slope Form Rewrite in slope-intercept form. Using (8, 1): y – y1 = m(x – x1) Method B Slope-intercept Form Rewrite the equation using m and b. Using (8, 1), solve for b. y = mx + b 1 = 3 + b b = –2

Let x = selling price and y = rent. Ex 4: The table shows the rents and selling prices of properties from a game. Express the rent as a function of the selling price. Let x = selling price and y = rent. Find the slope by choosing two points. Let (x1, y1) be (75, 9) and (x2, y2) be (90, 12). Selling Price ($) Rent ($) 75 9 90 12 160 26 250 44 To find the equation for the rent function, use point-slope form. y – y1 = m(x – x1)

Alg 2 2.4 Writing Linear Functions By comparing slopes, you can determine if the lines are parallel or perpendicular. You can also write equations of lines that meet certain criteria.

Write the equation of the line in slope-intercept form. Ex 5: Write the equation of the line in slope-intercept form. parallel to y = 1.8x + 3 and through (5, 2) m = 1.8 Parallel lines have equal slopes. y – 2 = 1.8(x – 5) Use y – y1 = m(x – x1) with (x1, y1) = (5, 2). y – 2 = 1.8x – 9 Distributive property. y = 1.8x – 7 Simplify. perpendicular to and through (9, –2) The slope of the given line is – 3/2, so the slope of the perpendicular line is the opposite reciprocal, 2/3. Use y – y1 = m(x – x1). y + 2 is equivalent to y – (–2). Distributive property. Simplify.