1 00:00:00,000 --> 00:00:00,580 2 00:00:00,580 --> 00:00:03,359 We're asked which of these lines are parallel. 3 00:00:03,359 --> 00:00:06,000 So they give us three equations of three different 4 00:00:06,000 --> 00:00:08,269 lines and if they're parallel, then they have to have the 5 00:00:08,269 --> 00:00:08,974 same slope. 6 00:00:08,974 --> 00:00:11,570 So all we have to do over here is figure out the slopes of 7 00:00:11,570 --> 00:00:12,830 each of these lines, and if any of them are 8 00:00:12,830 --> 00:00:14,060 equal, they're parallel. 9 00:00:14,060 --> 00:00:15,970 So let's do line A. 10 00:00:15,970 --> 00:00:21,870 Line A, it's 2y is equal to 12x plus 10. 11 00:00:21,870 --> 00:00:24,010 We're almost in slope-intercept form, we can 12 00:00:24,010 --> 00:00:29,210 just divide both sides of this equation by 2. 13 00:00:29,210 --> 00:00:33,420 We get y is equal to 6x-- right, 12 divided by 14 00:00:33,420 --> 00:00:36,329 2 -- 6x plus 5. 15 00:00:36,329 --> 00:00:38,859 So our slope in this case, we have it in slope-intercept 16 00:00:38,859 --> 00:00:43,710 form, our slope in this case is equal to 6. 17 00:00:43,710 --> 00:00:46,570 Let's try line B. 18 00:00:46,570 --> 00:00:51,810 Line B is y is equal to six. 19 00:00:51,810 --> 00:00:53,670 You might say this hey, this is a bizarre character, how do 20 00:00:53,670 --> 00:00:54,920 I get this into slope-intercept 21 00:00:54,920 --> 00:00:56,789 form, where's the x? 22 00:00:56,789 --> 00:00:59,679 And my answer to you is that it already is in 23 00:00:59,679 --> 00:01:00,640 slope-intercept form. 24 00:01:00,640 --> 00:01:05,670 I could just rewrite it as y is equal to 0x plus 6. 25 00:01:05,670 --> 00:01:08,170 The x term is being multiplied by 0 because the 26 00:01:08,170 --> 00:01:10,150 slope here is 0. 27 00:01:10,150 --> 00:01:12,130 y is going to be equal to six no matter how 28 00:01:12,129 --> 00:01:13,280 much you change x. 29 00:01:13,280 --> 00:01:15,689 Change in y is always going to be 0, it's 30 00:01:15,689 --> 00:01:17,879 always going to be 6. 31 00:01:17,879 --> 00:01:26,030 So here, our slope is 0, so these two lines are definitely 32 00:01:26,030 --> 00:01:29,060 not parallel, they have different slopes. 33 00:01:29,060 --> 00:01:31,689 So let's try line C. 34 00:01:31,689 --> 00:01:34,030 Line C-- I'll do it down here. 35 00:01:34,030 --> 00:01:40,780 Line C, so it's y minus 2 is equal to 6 times x plus 2. 36 00:01:40,780 --> 00:01:43,120 And this is actually in point-slope form, where the 37 00:01:43,120 --> 00:01:47,410 point x is equal to negative 2, y is equal to 2. 38 00:01:47,409 --> 00:01:50,909 So the point negative 2, 2, is being represented here because 39 00:01:50,909 --> 00:01:52,869 you're subtracting the points. 40 00:01:52,870 --> 00:01:56,590 And the slope is 6, so we already know that the slope is 41 00:01:56,590 --> 00:01:57,340 equal to 6. 42 00:01:57,340 --> 00:02:00,340 And sometimes people are more comfortable with 43 00:02:00,340 --> 00:02:03,109 slope-intercept form, so let's put it in slope-intercept form 44 00:02:03,109 --> 00:02:06,006 just to confirm that if we put it in this form, the slope 45 00:02:06,006 --> 00:02:07,239 will still be equal to 6. 46 00:02:07,239 --> 00:02:11,319 So if we distribute the 6, we get y minus 2 is equal to 6 47 00:02:11,319 --> 00:02:15,689 times x, 6x, plus 6 times 2 is 12. 48 00:02:15,689 --> 00:02:19,870 And if you add this 2 -- if you add 2 to both sides of the 49 00:02:19,870 --> 00:02:24,409 equation, you get y-- because these guys cancel out-- is 50 00:02:24,409 --> 00:02:27,329 equal to 6x plus 14. 51 00:02:27,330 --> 00:02:30,710 So you see, once again, the slope is 6. 52 00:02:30,710 --> 00:02:35,700 So line A and line C have the same the slope, so line A and 53 00:02:35,699 --> 00:02:37,099 line C are parallel. 54 00:02:37,099 --> 00:02:38,210 And they're different lines. 55 00:02:38,210 --> 00:02:39,460 If they had the same y-intercept, then they would 56 00:02:39,460 --> 00:02:41,490 just be the same line. 57 00:02:41,490 --> 00:02:41,933