Tutor profile: Jennifer R.
A line has a slope of 2 and passes through the point (0,6). What is the equation of the line in slope-intercept form?
This question requires us to use two different formulas - point-slope formula and slope-intercept formula. Point slope formula is used when we know the slope of a line and any point on the line. It is written y-y1=m(x-x1) where m represents the slope and y1 and x1 come from the point on the line (x1,y1). Slope-intercept formula is used when we know the slope of a line and the y-intercept. It is most commonly used to graph lines. The formula for it is y=mx+b where m represents the slope of the line and b represents the y-intercept (where the line passes through the y-axis). Now, let's look at the question. The question gives us the slope and one point on the line, so we need to start with the point slope formula. We know the slope is 2, so we will put in a 2 for the m in the formula. The point we are given is (0,6). Remember all ordered pairs are written in the form (x,y). That means the x in our point is 0 and the y is 6. We can plug those two numbers in for x1 and y1 in the formula respectively. y-6=2(x-0) To change this formula to slope-intercept, we need to start by using the distributive property to multiply our slope, 2, by what appears in the parenthesis. 2 times x = 2x and 2 times 0 = 0 Now we have y-6=x+0 The final step is to get y on a side by itself. To do that, we need to do the opposite of what is being done to y. This will have to be done on both sides to keep the equation equal. We can see that 6 is being subtracted from y. The opposite of subtracting 6 is adding 6 so we need to add 6 to both sides of the equation. -6 + 6 = 0 and 0 + 6 = 6 This leaves us with y=x+6 which is in slope-intercept form as the question asked.
Subject: Basic Math
1/10 + 1/10 + 5/10 =
Let's start with some fraction basics before beginning to solve this problem. The top number, or number above the bar, in a fraction is called the numerator. The bottom number, or number below the bar, in a fraction is called a denominator. The essential rule when adding fractions is that the denominator must be the same to add. When we look at this problem, we first need to look at the denominators, or bottom numbers. When we look we see that all of the denominators are 10. That is great! It means we are ready to add. To add fractions, once we have ensured the denominators are all alike, we want to add the numerators. In this problem we will be adding 1 + 1 + 5. 1 + 1 + 5 = 7. That will be the numerator of our answer. The denominator is not added. It stays the same. Since the denominator in each of these three fractions is 10, the denominator in the answer must also be 10. That leases us with an answer of 7/10.
Find the slope of the line that passes through (8, 8) and (3, 1).
This question requires the use of the slope formula. Slope formula is m=y2-y1/x2-x1. m represents slope. If we look at the question, we are given two distinct points (8,8) and (3,1). It does not matter which you decide is 1 or 2. Let's assign the first point, (8,8), and point 1. Let's assign the second point, (3,1), as point two. Quick reminder: every ordered pair is set up as (x,y). Let's plug these into the formula. m=1-8/3-8 From the first point, (8,8) y1=8 and x1=8 so I filled those in accordingly. In the second point, (3,1) x2=3 and y2=1 and so I plugged those in as well. Now we are ready to solve. First, we want to subtract the numerator, or top numbers. We have 1-8 which equals -7. That will be the numerator of our answer. Second, we want to subtract the denominator, or bottom numbers. We have 3-8 which equals -5. This will be the denominator of our answer. We have -7/-5. A fraction will never have two negatives. Remember that a fraction is a form of a division problem, so if we divide -7 by -5 we know that two negatives equal a positive. We do want to leave the actual fraction as an improper fraction, so our answer is 7/5. To take this a step forward, if you were to graph using a slope of 7/5 you would go up 7 spots and to the right 5 to go from one point to the next. Keep that in mind so when you are asked to graph using slope, you have a headstart.
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