1. Equations of Lines Given Two Points

2. 43210 In addition to level 3.0 and above and beyond what was taught in class, the student may: · Make connection with other concepts in math · Make connection with other content areas. The student will understand that linear relationships can be described using multiple representations. - Represent and solve equations and inequalities graphically. - Write equations in slope-intercept form, point-slope form, and standard form. - Graph linear equations and inequalities in two variables. - Find x- and y- intercepts. The student will be able to: - Calculate slope. - Determine if a point is a solution to an equation. - Graph an equation using a table and slope- intercept form. With help from the teacher, the student has partial success with calculating slope, writing an equation in slope- intercept form, and graphing an equation. Even with help, the student has no success understanding the concept of a linear relationships. Learning Goal #1 for Focus 4 (HS.A-CED.A.2, HS.REI.ID.10 & 12, HS.F-IF.B.6, HS.F- IF.C.7, HS.F-LE.A.2): The student will understand that linear relationships can be described using multiple representations.

3. Use the Slope Formula to Find the Equation of a Line Find an equation for a line that passes through these points (1,6) and (3,-4) First find the slope of the line. Let x 1, y 1 be (1,6) and x 2, y 2 be (3,-4). M = y 2 -y 1 = -4 – 6 = -10 = x 2 -y 1 3 – 1 2 -5

4. Now we know the m = -5, x = 1, and y = 6. Next solve for b. Substitute into y= mx + b. 6= (-5)(1) + b 6= -5 +b 11=b The y- intercept is b=11. So the final equation is: y = -5x + 11 Note - You can use either point in the equation and get the same answer.

5. Write an equation in slope-intercept form for the following points: (-3,2) and (5,-2). The slope of the line is: m = y 2 -y 1 = -2-2 = -4 = -1 x 2 -x 1 5-(-3) 8 2 To find the y- intercept, substitute the slope for -½ and use (-3,2 ) for (x,y) in the slope- intercept form. 2= (-1/2)(-3) + b 2= 3/2 + b ½= b

6. Now by using ½ as b and -½ as m, you can write the equation of the line: y= -½x + ½.