5-4 Point-Slope Form and Writing Linear Equations

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Presentation transcript:

5-4 Point-Slope Form and Writing Linear Equations Hubarth Algebra

Ex 1 Graphing Using Point-Slope Form The point-slope form of the equation of a nonvertical line that passes through the point (x1, y1) and has slope m is y – y1 = m(x – x1) Ex 1 Graphing Using Point-Slope Form 1 3 Graph the equation y – 2 = (x – 1). Start at (1, 2). Using the slope, go up 1 unit and right 3 units to (4, 3). Draw a line through the two points. 1 3 The equation shows that the line passes through (1, 2) with slope .

Ex 2 Writing an Equation in Point-Slope Form Write the equation of the line with slope –2 that passes through the point (3, –3). y – y1 = m(x – x1) Substitute (3, –3) for (x1, y1) and –2 for m. y – (–3) = –2(x – 3) Simplify the grouping symbols. y + 3 = –2(x – 3)

Ex 3 Using Two Points to Write an Equation Write equations for the line in point-slope form and in slope-intercept form. The slope is – . 1 3 First find the slope. = m y2 – y1 x2 – x1 4 – 3 –1 – 2 = – Second Use either point to write the equation in point-slope form. Use (–1, 4). y – y1 = m(x – x1) y – 4 = – (x – (– 1)) y – 4 = – (x + 1) 1 3 Third Rewrite the equation from Step 2 in slope–intercept form. y – 4 = – (x + 1) y – 4 = – x – y = – x + 3 1 3 2

Ex 4 Writing an Equation Using a Table Is the relationship shown by the data linear? If so, model the data with an equation. First Find the rate of change for consecutive ordered pairs. –2 –1 –6 –3 = 2 3 6 2 –1 –3 4 –2 –6 x y –1( ) –2 –3( ) –6 –2( ) –4 The relationship is linear. The rate of change is 2. Second Use the slope and a point to write an equation. y – y1 = m(x – x1) Use the point-slope form. y – 4 = 2(x – 2) Substitute (2, 4) for (x1, y1) and 2 for m.

Summary Slope-Intercept Form y = mx + b y = 3x + 5 Standard Form Ax + By = C 2x + 3y = 5 Point-Slope Form (y – y1) = m (x – x1) y – 1 = - 2 3 (x – 1)

Practice 1. Write the equation of the line that has a slope of 2 5 that passes through the point (10, -8) 𝑦+8= 2 5 (𝑥−10) 2. Write an equation of the line, in point-slope form, that has a slope of 2 that passes through the point (1, -5). Then rewrite in slope-intercept form. 𝑦+5=2(𝑥−1) 𝑦=2𝑥−7 3. Is the relationship shown by the data at the right linear? If so, model the data with an equation. Yes, its linear. 𝑦−5= 2 5 𝑥−19 x y -11 -7 -1 -3 4 19 5 4. Graph the equation 𝑦−5= 1 2 𝑥−2 . . . (4, 6) (2, 5)