Slope-Intercept Form

Slope

Key Terms Slope – The ratio between the amount of rise to the amount of “run”. The rate of change of a line. Y-Intercept – The point where a line crosses the y-axis on a coordinate plane. (x = 0 at this point) 3

Slope-Intercept Form of a Line A linear equation is in slope-intercept form when it has the form: y = mx + b, where m is the slope and b is the y-intercept. y-intercept slope y = mx + b

Identify slope & y-intercept y = 3x + 8 2. y = -2x + 4 y = ¾ x – 7 4. y = -4x 5. y = 5

Can you find the slope & y-intercept? 3x + 7y = -9

Converting to Slope-Intercept Solve the equation for y. 15x + 3y = 9 3y = -15x + 9 3 3 y = -5x + 3 Subtract 15x from both sides. -15x -15x Divide each term by 3. m = -5; b = 3

You Try: 1. 8x – 2y = 12 2. -18x + 3y = 15

Graph Using Slope-Intercept y = -5x + 3 m = -5 (slope); b = 3 (y-intercept) Step 1: Graph the y-intercept. Step 2: Slope is rise over run. -5 = Step 3: From y-intercept, go down 5, right 1 and graph 2nd point. Draw a line connecting the two points.

You Try: y = 4x – 3 2. y = 6x + 5

Guided Practice: p. 30-31 #1-11 Assignment:

Parallel Lines Parallel lines never intersect. Parallel lines have slopes that are equal (the same).

Example: Given: y = 3x -7 and y = 3x + 10 Find the slope of each. Both have a slope of 3. Therefore, the two lines are parallel.

Determine which of the functions represent parallel lines. (Hint: Rewrite each function in slope-intercept form.) 2x + 4y = 10 6x – 3y = -24 10x + 5y = -20 d. -16x + 8y = -56

Perpendicular Lines Perpendicular lines intersect at a right angle. The slopes of perpendicular lines are negative reciprocals of each other. Their product is -1.

Example: Given: y = ⅓x – 4 and y = -3x + 8 ⅓ and -3 are negative reciprocals. (⅓)(-3) = -1. Therefore, the two lines are perpendicular.

Determine which two lines are perpendicular. (Hint: Rewrite each equation in slope-intercept form.) -12x + 6y = -24 -8x + 2y = -6 16x + 4y = 8 3x + 12y = 84

Guided Practice: p. 31 #12 Assignment: