Warm Up Find each yintercept 1 y 3

Warm Up Find each y-intercept. 1. y = 3 x + 2 2. 5 x – 3 y = 12 Find each slope. 3. 4. Write this equation in y=mx+b form. 5. 4 x + 2 y = 10 6 x + 2 y = 6

Writing Equations of Parallel and Perpendicular Lines

Writing an equation in Slope intercept form (y=mx+b) given a slope and the y-intercept Example 1: Given: slope = 1; y-intercept = 0 Example 2: Given: rate of change = 0; y-intercept = -5

Writing an equation in Point-slope form given a slope and the y-intercept Examples : Write an equation in point-slope form for the line with the given slope that contains the given point. A. B. m = -2 and b = 3 m = 3/2 and C. m = 1 and ( 0 , -4 )

Remember from y=mx+b, we need a slope and a y intercept. What happens when we may know the slope, but we do not know the y - intercept? Well…If we know a SLOPE and a POINT that the graph passes through, we can use …. POINT-SLOPE FORMULA!

Writing an equation in Slope intercept form given 2 points Example 9: Write the equation that describes the line in slope-intercept form. Remember, we need an m and a b! Hint: Find slope first…Then use Point slope formula! (5, 7), (6, 8)

Writing an equation in Slope intercept form given a slope and a point Example 5: Write the equation that describes the line in slope-intercept form. m = ¾ , ( -4 , -1 )

Let’s recall what we know about parallel and perpendicular lines…

Parallel Lines SAME SLOPE but Different y-intercept y = 2 x+1 m=2 y = 3+2 x m=2 Slopes are NEGATIVE RECIPROCALS y = 2 x+1 m=2 Horizontal Lines are parallel y = -2 y=8 m=0 Perpendicular Lines m=0 Vertical Lines are parallel x=3 x = -4 m = undefined y = 3 - ½x m=-½ Vertical and Horizontal Lines are perpendicular to each other y = -4 x=1 m = 0 m = undefined

Example 1 Write the equation of the line with a y-intercept of -2 and parallel to y = 4/5 x. Step 1 Find the slope of the new line. Step 2 Write the equation in slope-intercept form using y = mx + b or y – y 1 = m(x – x 1)

Example 2 Write the equation of the line with a yintercept of 4 and perpendicular to y = 2 x + 1. Step 1 Find the slope of the new line. Step 2 Write the equation in slope-intercept form using y = mx + b or y – y 1 = m(x – x 1)

Example 3 Write an equation in slope-intercept form that is perpendicular to the graph and has a y-intercept of -3. y 7 6 5 4 3 2 1 x − 6 − 5 − 4 − 3 − 2 1 − 1 − 2 − 3 − 4 − 5 − 6 2 3 4 5 6 7

Example 4 Write an equation in slope-intercept form for the line that passes through (4, 10) and is parallel to the line described by y = 3 x + 8. Step 1 Find the slope of the new line. Step 2 Write the equation in slope-intercept form using y = mx + b or y – y 1 = m(x – x 1)

Example 5 Write an equation in slope-intercept form for the line that passes through (2, – 1) and is perpendicular to the line described by y = 2 x – 5. Step 1 Find the slope of the new line. Step 2 Write the equation in slope-intercept form using y = mx + b or y – y 1 = m(x – x 1)