2.4 Writing Equations of Lines

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Presentation transcript:

2.4 Writing Equations of Lines

In this lesson you will: Write linear equations. Write direct variation equations.

Writing an Equation of a Line You can write the equation of a line using one of the following handy-dandy formulas: Slope-Intercept form: (Given the slope m and the y-intercept b) use this equation): Point-Slope Form: (Given the slope m and a point (x1,y1), use this equation): In calculus we consider this formula to be one of our “best friends.” Two Points: (Given two points (x1,y1) and (x2,y2), use the equation) Use this formula to find the slope m, then use the point-slope form with this slope and either of the given points to write an equation of the line.

Write the equation of the line shown: The y – intercept is -2 The slope is 3/2 y = (3/2)x-2

And finally simplify to y = (-1/2)x+4 Write the equation of the line that passes through (2,3) and has slope -1/2. Use the point-slope formula: y-3=(-1/2)(x-2) And finally simplify to y = (-1/2)x+4

Write the equation of the line that passes through (3,2) and is a) perpendicular and b) parallel to y = -3x + 2. The parallel line will have slope -3 and the perpendicular line will have slope 1/3. Perpendicular Parallel y=(1/3)x+1 y-2=-3(x-3) y = -3x+11 y-2=(1/3)(x-3)

Write the equation of the line that passes through (-2,-1) and (3,4) First determine the slope: You now know the slope and can use either of the given points in the point-slope formula. Would you get the same answer if you used either given point? y = x + 3

Two variables show direct variation provided y=kx and k is not 0. K is called the constant of variation and y is said to vary directly with x. The graph of y = kx is a line through the origin. The variables x and y at the right vary directly, and y=12 when x=4. Write an equation relating x and y. Find y when x is 5. (5,15) (4,12) Note: In direct variation the ratio y/x is constant.

Does the data show a direct variation between x and y? This data shows information about 14-karat Gold Chains (1 gram per inch) Length, x (inches) 16 18 20 24 30 Price, y (dollars) 288 324 360 432 540 Does the data show a direct variation between x and y? To decide if there is a direct variation, check whether the quotient of y and x is constant. Yes, the data shows direct variation and the direct variation equation is y = 18x.

Does the data show direct variation? Loose Diamonds (round, colorless, very small flaws) Weight, x (carats) 0.5 0.7 1.0 1.5 2.0 Price, y (dollars) 2250 3430 6400 11,000 20,400 Does the data show direct variation?

Homework 13-57 odd, 59, 63