1. EQUATIONS OF STRAIGHT LINES Find the equation of the line that has slope 3 and y-intercept (0,2) This is easy because the slope-intercept form of a line, y=mx +b, has m=slope, and b = the y-coordinate of the y-intercept. So plugging in m=3 and b=2, we get y = 3x + 2 Example 2: Find the equation of the line that passes throught the point whose coordinates (-2,-1) and slope = 3/2. USE THE POINT-SLOPE FORMULA. Recall that the slope, m, can be found by this equation: Now we plug in the slope and the given point into this equation. m=3/2 and (x 1,y 1 ) = (-2,-1)

2. FIND THE EQUATION OF A LINE GIVEN TWO POINTS We need a point and a slope to use the point-slope formula. So this type of problem requires 2 steps: Step 1) Find the slope using the two points, (x 1,y 1 ) and (x 2,y 2 ) and the formula: Step 2) Use one of the given points and the slope you just found in the Point-slope formula and then get y by itself. Example 3: Find the equation of the line that passes through the points whose coordinates are (-4,-5) and (8,4) Step 1) Find the slope. Let (x 1,y 1 ) = (-4,-5) and (x 2,y 2 )=(8,4) Step 2) Use the point-slope formula and get y by itself.

3. FIND THE EQUATION OF A LINE GIVEN THAT IT IS PARALLEL OR PERPENDICULAR TO ANOTHER LINE. First, know these facts: A.Parallel lines have the same slope. B.The slopes of Perpendicular lines are negative reciprocals. Second, use the same steps as before. Step 1) Find the Slope of the line you are finding. Step 2) Use the Point-Slope Formula and get y by itself to make an equation. Worksheet Part 4 Letter C Write an equation for the line that is parallel to 4x + y = -9 and contains the point (-2,9) Step 1) Find the slope If a line is parallel to 4x+y=-9, that means it has the same slope. What is the slope of 4x+y=-9? Don’t assume it’s 4, because this is not in slope-intercept form. Get y by itself for slope- intercept form. y = -4x – 9 Slope = -4 Now we know the parallel line’s slope is -4 the given point lying on that line is (-2,9) Step 2) Use the Point-Slope Formula y-9 = -4(x-(-2)) y-9 = -4(x+2) y-9 = -4x -8 y = -4x + 1

4. Worksheet Part 5 Letter M Write an equation for the line that is perpendicular to the line, 3x + 2y = -10 that contains the point (-9,-2) Step 1) Find the Slope Lines that are perpendicular have slopes that are opposite reciprocals. What’s the slope of the first line? 3x + 2y = -10 2y = -3x – 10 So the slope of a line perpendicular to this is ⅔ Step 2) Use the Point-Slope Formula using m=⅔ and the given point, (-9,-2)