Writing and Graphing Linear Equations
- 1. Module 5 Lesson 3 Questions that are Similar to Those on Your Mastery Assignment
- 2. 1. Write the equation of the line through the points (6, 3) and (6, -8). The x-coordinates of these points are the same, meaning this is a vertical line. The equation would be x = 6.
- 3. 2. Are the equations parallel, perpendicular, or neither? 5𝑥 = 𝑦 − 4 13 + 5𝑦 = −𝑥 We need to put them in y = form before we compare to make our decision. The first one would say y = 5x + 4. The second one would first say 5y = -x – 13. Then we would divide by 5 to get y = -1/5x – 13/5. Since the slope of our first line is 5, and the second line is -1/5, these are opposite reciprocal slopes. This means our lines are perpendicular.
- 4. 3. Describe the graph of y = -2. This is a horizontal line that passes through y = -2.
- 5. 4. Are the equations parallel, perpendicular, or neither? 𝑦 = −6𝑥 + 2 −6𝑦 = 𝑥 + 4 We need to put them in y = form before we compare to make our decision. The first one already is, and the second one would say y = -1/6x – 4/6. Since the first line has a slope of -6 and the second one has a slope of -1/6, these lines are neither…they aren’t the same slopes, nor are they opposite reciprocals.
- 6. 5. Describe the graph of x = 2. This is a vertical line that passes through x = 2.
- 7. 6. Write the equation of the line through (-8, -4) and (12, -4). The y-coordinates of these points are the same, meaning this is a horizontal line. The equation would be y = -4.
- 8. 7. Write the equation in standard form through (-2, 1) and (5, -5). First, find the slope: 𝑚 = −5−1 5−(−2) = −6 −7 = 6 7 Then, pick a point. I’ll use (-2, 1). Next, plug into point-slope form and solve for y: 𝑦 − 1 = 6 7 𝑥 + 2 𝑦 − 1 = 6 7 𝑥 + 12 7 𝑦 = 6 7 𝑥 + 19 7 To put it in standard form, move the x term over with the y term, and then make sure that the first number isn’t a fraction or negative. If it is, make it a positive number that isn’t a fraction: − 6 7 𝑥 + 𝑦 = 19 7 6𝑥 − 7𝑦 = −19
- 9. 8. Find the x-intercept of 8x + 3y = 16. The x-intercept happens where y = 0, so plug in 0 for y and solve. 8x + 0 = 16 8x = -16 x = -2 The x-intercept would be (-2, 0).
- 10. 9. Find the y-intercept of -2x – 3y = 12. The y-intercept happens where x = 0, so plug in 0 for x and solve. 0 – 3y = 12 -3y = 12 y = -4 The y-intercept would be (0, -4).
- 11. 10. Write 𝑦 − 2 = 2 3 (𝑥 − 4) in standard form. Like in #7, first put it in y = form and then rearrange. 𝑦 − 2 = 2 3 𝑥 − 8 3 𝑦 = 2 3 𝑥 − 2 3 − 2 3 𝑥 + 𝑦 = − 2 3 2𝑥 − 3𝑦 = 2