2. Point-Slope Form of Linear Equations Suppose you know that a line passes through the point (3,4) with a slope of 2. You can quickly write an equation of the line using point-slope form. ( y - y 1 ) = m ( x - x 1 ) ( x 1 , y 1 ) is a point on the line and m is the slope. So the difference in y equals the slope times the difference in x. m = ( y - y 1 ) ( x - x 1 )
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4. Write an equation in point-slope form of the line that passes through the point (2, 5) and has a slope of 3. ( y - y 1 ) = m ( x - x 1 ) Substitute the 5 in for y 1 , the 2 in for x 1 and the 3 in for m. ( y - 5 ) = 3 ( x - 2 )
5. Graphing Using Point-Slope form Graph the equation ( y - 1) = 2/3( x - 3). The equation shows that the line passes through the point (3, 1) with a slope of 2/3. Start at (3, 1), go up 2 units and right 3 units. Draw your line.
6. Now you try Graph the equation y - 4 = 2( x - 3) Start at (3, 4) go up 2 and right 1.
7. Now you try: Write the equation of the line with a slope of -3 that passes through the point (-1, 7) in point-slope form. ( y - 7) = -3( x + 1) Write the equation of the line with a slope of 2/3 that passes through the point (10, -8). y + 8 = 2/5(x - 10)
8. Write the equation of the line in point-slope form and in slope-itercept form. (2,3) (-1, -5)
9. If you know two points on a line, first use them to find the slope. Then use either point to write the equation. Find write the equations for the line in point-slope form and in slope-intercept form given the points (2, 3) and (-1, -5). Step 1: Find the slope. -5 - 3 = 8 -1 - 2 3 Step 2: Use either point to write the equation in point-slope form. y - 3 = 8/3( x - 2) Step 3: Rewrite the equation in slope-intercept form. y - 3 = 8/3( x - 2) y - 3 = 8/3x - 5 1/3 y = 8/3x - 2 1/3 Now you try step 2 and 3 with the point (-1, -5)
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12. You can write a linear equation to model data in tables easily with point-slope form. Consider the following data table. What is the slope? Choose one data pair to use as point. 10 11 7 5 6 3 4 -1 y x
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