Write the equation of a straight line which is parallel to y=4x+2 ?
To start this question, let us remember the equation of a straight line, y = mx + b, where m is the slope and b is the y intercept. In general terms, the slope is how sharp the line rises or falls, and the y intercept is where the line crosses the y axis. We know parallel lines must never intercept each other, and using that fact we can deduce that parallel lines must have the same slope. If two lines have the same slope, they will rise or fall at the same rate, ensuring they never touch. So we know m must equal 4. But what about b? Thats what makes this question easy! b can be any number you'd like, provided you dont choose two, or they would be the same line. No matter where on the y axis our line intercepts, so long as it has the same slope, our lines will never intersect!
1/8 + 1/2 = ?
For this problem, we are trying to find the sum of the fractions 1/8 and 1/2. To do this, we must put our fractions in a form where they can be added, this is known as finding a common denominator. Lets look at the numbers 8 and 2, do we know a number that both of them fit into? I can think of a few off the top of my head, 8, 16, 24.... 8 and 2 all fit into those. We can use any of those numbers to complete this problem, but choosing the smallest number (8) will make this problem as simple as possible. This is because 1/8 already has a denominator of 8, so we do not have to change it. This means that we only have to alter 1/2. How do we do this? Well we already know to change the denominator to 8, since we decided that 8 was our common denominator. So now all we need to do is change the numerator. Imagine looking at a pizza pie, cut into 8 slices. The question we must ask ourselves is, how many slices of that pie will equal half the pie? Visually, if we cut the pizza pie in half, we know the answer is 4 slices. But to solve it mathematically, we must figure out how many times 2 goes into 8. The answer is 4, and that is the numerator. We now know 1/2 is equivalent to 4/8. Our question now looks like 1/8 + 4/8 = ? We add the numerators like normal, and the denominator stays the same (remember: we are dealing with a pizza pie with 8 slices). Which means our answer is 5/8!
2x + 6 = 4x - 2
Looking at this problem, we can solve it in a variety of different ways. We can manipulate the terms with x, by moving them to one side and factoring them out, or we can manipulate the single terms. Its up to you. Personally, I would first solve this problem by dealing with the terms that do not contain x. If we look at the right hand side of this equations, we find we can take the -2 away by adding a +2 to each side of the equations. When we add our like terms, our new equation will look like 2x + 8 = 4x. Now we can deal with the terms that contain x. We can use the same method as before, however this time our like terms will be those that contain x. Lets move 2x to the right side of the equation by subtracting -2x from the left side and adding it to the right. Our equation now looks like 8 = 2x. Our goal from the beginning has always been to get the x by itself, and we can now achieve that by removing the 2 from the right side. Since 2 and x are being multiplied, we can divide 2 to cancel it on the left. This yields 4 = x, and the problem is completed.