2.5 Writing Equation of a Line Sept 19, 2012

Equations of a Line equation written in the form Ax + By = C where A and B are not both zero Slope-Intercept Form equation written in the form y = mx + b where m is the slope and b is the y-intercept. Point-Slope Form equation written in the form y - y 1 =m(x - x 1 ) where (x 1, y 1 ) is a point on the line and m is the slope. Standard Form

Example 1 Write an Equation Given a Graph Write an equation of the line in slope intercept form. From the graph, you can see that the slope is. Because the line intersects the y-axis at, the y-intercept is SOLUTION ( 0, 2 – ) 5 3 m = 2. b = –

Example 1 Write an Equation Given Slope and y -Intercept () 2 – x 5 3 y = + Substitute for m and for b. 2 – 5 3 x 5 3 y = 2 – Simplify. Use slope-intercept form to write an equation of the line. y x = + mb Use slope-intercept form.

Write an equation of the line in slope intercept form.

Checkpoint 1. ANSWER = y 1+3x3x 2. m = 2,2, 4b = –– ANSWER = y 4–2x2x – m = b= 5 –, 3,3, m = 1b = Write an equation of the line that has the given slope and y -intercept. ANSWER = y 5–x 2 1 Write an Equation Given Slope and y -Intercept

Writing Equation of a line given 1.Write the equation of the line in point slope form y - y 1 =m(x - x 1 ) by substituting the point for x 1, y Simplify the right side using distributive prop. 3. Isolate y by getting rid of y 1. slope and a point

Example 2 Write an Equation Given Slope and a Point Use point-slope form. = y y 1 – () x x 1 – m = y 2 – 4 1 – () 4x – = – 4 1 – 1x + Distributive property = y – x + Slope-intercept form SOLUTION x 1, y 1

OR 1.Substitute the x-coordinate of the point for x and y-coordinate for y and the slope for m in the equation y= mx + b. 2.Solve for b. 3.Now that you have b and m, write the equation of the line in y = mx + b slope and a point

Example 2 Write an equation of the line that passes through (4, 2) and has a slope of. 4 1 – = y – x + y = mx + b 2 = -¼ (4) + b 2 = -1 + b +1 3 = b Substitute 2 for y, 4 for x and -¼ for m Simplify Solve for b

Checkpoint Write an equation of the line that passes through the given point and has the given slope. Write your equation in slope-intercept form. ANSWER 5 = 2x2xy+ 7 = 3x3xy+ – 14 = 5x5xy+ ANSWER = y 3 2 x1 – Write an Equation Given Slope and a Point 4. () 31,1, – = m2, 5. () 4,4, 5 – = m3 –, () 42,2, – = m5 6., () 3,3, – 3 – = m ,

Find the Equation of the Line Given Two Points ● Calculate the slope of the two points. ● Use one of the points and the slope to substitute into the Point-Slope formula. y - y 1 =m(x - x 1 ) ● Rewrite the equation in y = mx + b form.

Example ● Write the equation of the line that goes through the points (3, 2) and (5, 4).

Checkpoint ● Write the equation of the line that goes through the points (4, -1) and (2, -2).

Checkpoint ● Write the equation of the line that goes through the points (6, -3) and (-4, 2).

Homework : 2.5 p.97 #13-33odd, 45, 47