5 4 PointSlope Form and Writing Linear Equations
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5 -4 Point-Slope Form and Writing Linear Equations Hubarth Algebra
Point-Slope Form The point-slope form of the equation of a nonvertical line that passes through the point (x 1, y 1) and has slope m is y – y 1 = m(x – x 1) Ex 1 Graphing Using Point-Slope Form 1 Graph the equation y – 2 = 3 (x – 1). The equation shows that the line passes through (1, 2) with slope 1. 3 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.
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 – y 1 = m(x – x 1) y – (– 3) = – 2(x – 3) y + 3 = – 2(x – 3) Substitute (3, – 3) for (x 1, y 1) and – 2 for m. Simplify the grouping symbols.
Ex 3 Using Two Points to Write an Equation Write equations for the line in point-slope form and in slope-intercept form. First find the slope. y 2 – y 1 x 2 – x 1 =m 4– 3 1 =– – 1 – 2 3 1 The slope is –. 3 Second Use either point to write the equation in point-slope form. Third Rewrite the equation from Step 2 in slope–intercept form. Use (– 1, 4). y – 4 = – 1 (x + 1) y – y 1 = m(x – x 1) y – 4 = – 1 x – 1 y– 4=– 1 (x – (– 1)) 3 y – 4 = – 1 (x + 1) 3 3 3 y=– 2 1 x+3 3
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. x y – 2 =2 3 6 – 1( ) – 2 2 4 – 3( ) – 6 =2 – 1 – 2( ) – 4 – 3 – 6 – 2 =2 – 1 The relationship is linear. The rate of change is 2. Second Use the slope and a point to write an equation. y – y 1 = m(x – x 1) Use the point-slope form. y – 4 = 2(x – 2) Substitute (2, 4) for (x 1, y 1) and 2 for m.
Practice 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. 3. Is the relationship shown by the data at the right linear? If so, model the data with an equation. x y . . (2, 5) (4, 6) -11 -7 -1 -3 4 -1 19 5
