Explanation:
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To find the equation of a line in point slope form, we need two things: a point and a slope.
Luckily, we have two points, so we can use them to calculate the slope.
The slope is the change in y divided by the change in x, or rise over run. In this case, the rise is -10 - (-8) = -2 and the run is -4 - 6 = -10.
So the slope is -2 / -10 = 1/5. Now we can use any of the given points and plug them into the point slope formula, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point.
Let's use (6, -8) as our point. Then we get y - (-8) = (1/5)(x - 6), which simplifies to y + 8 = (1/5)x - 6/5.
And that's it! We have found the equation of the line in point slope form.
But wait there's more
How would you turn this into slope intercept form: y + 8 = (1/5)x - 6/5.
Well, first of all, you need to get rid of that pesky 8 on the left side. How do you do that? You subtract 8 from both sides, of course! That's the golden rule of algebra: whatever you do to one side, you have to do to the other. Otherwise, the equation gets angry and starts spitting out wrong answers. So, after subtracting 8, you get:
y = (1/5)x - 6/5 - 8
Now, you have to simplify the right side. You can't have fractions and whole numbers mixed together like that. It's like putting pineapple on pizza. So, you have to convert 8 into a fraction with the same denominator as the other fractions. In this case, that's 5. How do you do that? You multiply 8 by 5/5, which is the same as multiplying by 1. So, you get:
y = (1/5)x - 6/5 - 40/5
Now, you can combine the fractions by subtracting their numerators and keeping their denominators. That gives you:
y = (1/5)x - 46/5
And there you have it! You have turned the equation into slope intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 1/5 and the y-intercept is -46/5. Congratulations! You have solved a math problem and learned something new. And hopefully, you had some fun along the way.