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 ) 1313 The equation shows that the line passes through (1, 2) with slope. 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. Ex 1 Graphing Using Point-Slope Form

Simplify the grouping symbols.y + 3 = –2(x – 3) Write the equation of the line with slope –2 that passes through the point (3, –3). y – y 1 = m(x – x 1 ) Substitute (3, –3) for (x 1, y 1 ) and –2 for m. y – (–3) = –2(x – 3) Ex 2 Writing an Equation in Point-Slope Form

The slope is – First find the slope. = m y 2 – y 1 x 2 – x 1 4 – 3 –1 – 2 = – 1313 Write equations for the line in point-slope form and in slope-intercept form. Ex 3 Using Two Points to Write an Equation Second Use either point to write the equation in point-slope form. Use (–1, 4). y – y 1 = m(x – x 1 ) y – 4 = – (x – (– 1)) y – 4 = – (x + 1) Third Rewrite the equation from Step 2 in slope–intercept form. y – 4 = – (x + 1) y – 4 = – x – y = – x

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

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. xy (2, 5) (4, 6)