Write an equation for each line passing through the given pair of points. Give the final answer in $(a)$ slope-intercept form and (b) standard form. See Example 7 ....

Write an equation for each line passing through the given pair of points. Give the final answer in $(a)$ slope-intercept form and (b) standard form. See Example 7 . $(-2,-1)$ and $(3,-4)$

We have a line going through the points for 10 and 6 12 And we're trying to make an equation for the line in both slope intercept form and standard form. Well, all that we have are two points, so you gotta start by finding slope change. Of why so 12 minus 10 over. Change of X six minus four and then simplify 12 minus 10 is to six. Minus four is too. So slope is one. Now we don't have a y intercept, so we're going to use point slope form appear. So we're gonna pick this point here as our X one in our why one or you could have chosen 6 12 It's up to you. Either way, we'll get there. So let's plug in four and 10 as our x one and why one? So we're gonna say why minus 10 equals one times parentheses, X minus four. That just means why minus 10 equals X minus four, and we want slope intercept form. So get why by itself and we're left with y equals X plus six guts for part A, that's the slope intercept form and then turning that into standard form. So for part B. If we start with Y equals X plus six and we want standard form, we have to get X and Y together on the same side so we could go minus X if we want. So that's negative. X plus y equals six, but it's standard to have X being positive. So if you go times negative one on both sides, you end up with positive X minus y equals negative six or early on here. You could have attracted wife from both sides and then sprinted X from both sides and gotten the same thing. So your steps convey Ari for how you get to standard form. But just get your ex first than your why and then your number, and it's best to have acts being positive.

We have a line going through the points 85 and 96 And we want to write the equation for that line First and slope intercept form. And then in standard form, we can't start with slope intercept form boat, though, because we don't know the Y intercept. All we can do for our first step is find Slope. So change of why So that six minus five over change of X nine minus eight six minus five is 19 minus eight is one source slope is one. And then pick one of the points and call that your X one y one. And we're gonna do point slope formula. No. So we're gonna write why minus five equals M times parentheses, X minus X one. So you really have y minus five equals X minus AIDS. No, get why by itself for slope intercept form. So ab five, then you get why equals X minus three? Because negative eight plus five is negative three. So why equals X minus three is your answer for part A And then for part B, we're gonna take that equation and put it into a standard form. So, accent, why on the same side. I'll do it a little different this time. You can go minus. Why? For your first step if you want, then you have zero equals X minus Y minus three and the three needs to be added. So it goes all by itself on that side. And then you have three equals X minus y, and then swap your left and right sides. Now you have the same equation, but you have standard form.

We want the equation for the lion through negative 40 and 02 and we want it first and slope intercept form and then in standard form, if you notice this right here. Is that why intercept 02 is on the Y axis. That means B equals two. So if I have a slope and the Y intercept, I can make slope intercept form. We gotta find our slope. So do change of why? To minus zero. Over. Change of X. Tu minus zero is 20 minus negative. Four means plus four. So that's 1/2. Now that I have B and I have my slope, I can use that right now. So for part a, my answer is why equals 1/2 X plus two upload in m and B that I found for part B. We're gonna take that same equation, and we're gonna turn it into standard for him. So it's not good to have a fraction times your ex for standard form. So let's go times two and clear our fractions. So that's two. Why equals we're gonna distribute half times two is just one. So that's one X and then plus four and we want to get accident. Why? On the same side. So I have zero equals X minus two y plus four. I need to get the four by itself on the other side. So now I have negative for equals. X minus two. Why now? Just slop your left and right sides. And now you have standard form.

I want the equation through the 0.0 negative two and negative 30 And I want it both in slope intercept form and then in standard form. If you look at the two points, this is a why intercept. So that means B is negative. Two, we've gotta find Slope. So the change of why over change of X and then simplified zero minus negative to mean zero plus two. The negative three minus zero is just negative three. So it's a negative slope of 2/3. Now that we have slope and why intercept? We can go ahead and answer part A using this formula. So why equals my slope, Times X plus my Y intercept. So plus a negative two is like saying minus two. So that's the answer for part a. Then for part B, you gonna take that same equation and turn it into standard form. So you want to clear your fraction by the X. So go times three on both sides. So you get three. Why equals and you're gonna distribute negative 2/3 times three is negative two and then two times three is six as negative. We want X and Y on the same side. So I want to add two X and I want the extra come first as positives as positive two x and a positive three y. And on this side, I just have a negative six, and now it's in standard form.