1. ALGEBRA – LESSON 107 Equation of a Line with a Given Slope Be ready to grade the homework!

2. Equation of a line We have been writing equations based on knowing the slope and the y-intercept. This is called the Slope-intercept form: y = mx + b We need to have another way to figure out an equation. If we know 1 point on the line and the slope of the line, then we can write an equation in another form Point-slope form: y-y 1 = m(x-x 1 ) If we are not given a slope, we may need to calculate it from two given points slope: y 1 – y 2 x 1 – x 2 Note that all of these formulas are on your red reference sheet. Please start bringing that to class every day, including test days.

3. Equations of a line: y - y 1 = m(x - x 1 ) Find the equation of the line that passes through the point (4, -4) and has a slope 2. y + 4 = 2(x - 4) m = 2, x = 4, y = -4 #1 If the question says “write the equation”, they will mean slope-intercept form. y + 4 = 2x - 8 y = 2x - 12

4. Equations of a line: y - y 1 = m(x - x 1 ) Find the equation of the line that passes through the point (-1, -2) and has a slope -4. y + 2 = -4(x + 1) m = -4, x = -1, y = -2 #2 y + 2 = -4x - 4 y = -4x - 6 You should be able to graph this line either from the information given or by re-writing the equation.

5. Equations of a line: y - y 1 = m(x - x 1 ) Find the equation of the line that passes through the point (-2, 3) and has a slope 3. Use the equation and plug in the given values. y – 3 = 3(x + 2) m = 3, x = -2, y = 3 #3 Sometimes you will be asked to leave it in this form. But you’ll usually have to keep going. y – 3 = 3x + 6 y = 3x + 9

6. Equations of a line: y - y 1 = m(x - x 1 ) Find the equation of the line that passes through the point (2, -2) and is parallel to the line y = 3x + 3. y + 2 = 3(x - 2) m = 3, x = 2, y = -2 #4 y + 2 = 3x - 6 y = 3x - 8 If lines are parallel, they have the SAME SLOPE. If they are perpendicular, the slopes are OPPOSITE RECIPROCALS.

7. Equations of a line: y - y 1 = m(x - x 1 ) Find the equation of the line that passes through the point (1, -1) and is parallel to the line y = -3x + 7. y + 1 = -3(x - 1) m = -3, x = 1, y = -1 #5 y + 1 = -3x + 3 y = -3x + 2 If lines are parallel, they have the SAME SLOPE. If they are perpendicular, the slopes are OPPOSITE RECIPROCALS.

8. Equations of a line: y - y 1 = m(x - x 1 ) Find the equation of the line that passes through the point (2, -2) and is perpendicular to the line y = 2x + 3. y + 2 = -½(x - 2) m = -1/2, x = 2, y = -2 y + 2 = -½x + 1 y = -½x – 1 If lines are parallel, they have the SAME SLOPE. If they are perpendicular, the slopes are OPPOSITE RECIPROCALS.

9. Homework: Worksheet