1. Writing Equations of Lines
Slope-Intercept Form

2. Equations of Lines
Remember the equation of a line is: y = mx + b We have to have both a “m” and a “b” to write an equation. If you are given two points, you can find the slope and the y-intercept to write the equation. Write the equation of the line that passes through (5,4) and (6,9). m = (𝟗 −𝟒) (𝟔 −𝟓) = 𝟓 𝟏 =𝟓 9 = 5(6) + b 9 = 30 + b b = -21 y = 5x - 21
Find the slope using the slope formula.
Plug in one of the points to find “b”.
Write the equation.

3. Equations of lines Try two on your own…… (-5,-2) and (4,-1)
y = 1/9x – 13/9
(3,8) and (-4,-5)
y = 13/7x + 17/7

4. Equations of Lines
We can also write equations of lines given other information. Remember from geometry: Parallel lines have the same slope. Perpendicular lines have slopes that are opposite reciprocals. Opposite reciprocal: if the slope is 3, the opposite reciprocal is -1/3.

5. Equations of Lines
Write the equation of the line that passes through (4,2) and is parallel to y=2x + 4. If the lines are parallel, the slopes are the same. The slope of the new line is m=2. Now just like before, solve for “b”. 2 = 2(4) + b 2 = 8 + b b = -6 So,……. y = 2x - 6

6. Equations of Lines
Write the equation of the line that passes through (4,7) and is perpendicular to y = -2x + 9. The new slope is m = ½ (opposite reciprocal) Now finish like all of the other problems….. 7 = ½(4) + b 7 = 2 + b b = 5 y = 1/2x + 5

7. Equations of lines
Your turn……
Write the equation of a line that passes through the point (-2,-3) and is parallel to y=4x – 7.
y = 4x + 5
Write the equation of a line that passes through the point (7,1) and is perpendicular to y=4x + 2.
y = -1/4x + 11/4