1. WARM-UP Solve each equation for y 1) 2) Determine if the following points are on the line of the equation. Justify your answer. 3) (3, -1) 4) (0, 1)

2. WARM-UP Solve each equation for y 1) 2) Determine if the following points are on the line of the equation. Justify your answer. 3) (3, -1) 4) (0, 1) YES NO

3. NOTES: Writing the equation of a line in point- slope form Day 1 Algebra

4. Let’s remember the different slopes possible… Positive Slope x y m > 0 Line rises from left to right. Zero Slope x y m = 0 Line is horizontal. m is undefined Undefined Slope x y Line is vertical. Negative Slope x y m < 0 Line falls from left to right.

5. Point-Slope Form of the Equation of a Line The point-slope equation of a non-vertical line of slope m that passes through the point (x 1, y 1 ) is y – y 1 = m(x – x 1 ). The point-slope equation of a non-vertical line of slope m that passes through the point (x 1, y 1 ) is y – y 1 = m(x – x 1 ).

6. Point Slope Formula The point-slope formula y – y 1 = m(x – x 1 ). m = slope The point-slope formula y – y 1 = m(x – x 1 ). m = slope

7. Example 1 Write an equation of the line in point-slope form that passes through the given point and has the given slope: m = –8, (7, –7) Step 1: Write down the formula

8. Example 1 Write an equation of the line in point-slope form that passes through the given point and has the given slope: m = –8, (7, –7) Step 2: Substitute the given slope

9. Example 1 Write an equation of the line in point-slope form that passes through the given point and has the given slope: m = –8, (7, –7) Step 3: Substitute the given point

10. Example 1 Write an equation of the line in point-slope form that passes through the given point and has the given slope: m = –8, (7, –7) Step 4: Simplify

11. Column Questions???

12. Example 2 Write an equation of the line in point-slope form that passes through the given point and has the given slope: m = 4, (3, 1) Step 1: Write down the formula

13. Example 2 Write an equation of the line in point-slope form that passes through the given point and has the given slope: m = 4, (3, 1) Step 2: Substitute the given slope

14. Example 2 Write an equation of the line in point-slope form that passes through the given point and has the given slope: m = 4, (3, 1) Step 3: Substitute the given point

15. Example 2 Write an equation of the line in point-slope form that passes through the given point and has the given slope: m = 4, (3, 1) Step 4: Simplify

16. Column Questions???

17. Example 3: Writing the Point-Slope Equation of a Line YOU TRY!! Write the point-slope form of the equation of the line passing through (-1,2) with a slope of 4. Then solve the equation for y. Solution We use the point-slope equation of a line with m = 4 and (-1, 2). This is the point-slope form of the equation. y – y 1 = m(x – x 1 ) Substitute the given values. Simplify. y – 2 = 4[x – (-1)] We now have the point-slope form of the equation for the given line. y – 2 = 4(x + 1) Y – 2 = 4x + 4 Y = 4x + 6 Solve for y. This is called slope-intercept form.

18. Example 4: Writing the Point-Slope Equation of a Line YOU TRY!! Write the point-slope form of the equation of the line passing through (-5,-2) with a slope of -4. Then solve the equation for y. Solution We use the point-slope equation of a line with m = -4 and (-5, -2). This is the point-slope form of the equation. y – y 1 = m(x – x 1 ) Substitute the given values. Simplify. y – (-2 )= -4[x – (-5)] We now have the point-slope form of the equation for the given line. y + 2 = -4(x + 5)

19. Summary and Column Questions???