+2446 To determine the intercepts of this equation in the form \(ax+by+c=0\), I would just make x and y zero and see what the result is:
Finding the x-intercept
For a line without the slope of 0, the line only touches the x-axis once. For a point to be on the x-intercept, y must be zero; otherwise, it would not be on the x-intercept. Knowing this, you can set the y to be zero and solve for x:
| \(4x+5y+6=0\) | Make y=0 so that the point is on the x-intercept. |
| \(4x+5*0+6=0\) | |
| \(4x+6=0\) | Subtract 6 on both sides. |
| \(4x=-6\) | Divide by 4 on both sides. |
| \(x=\frac{-6}{4}=-\frac{3}{2}=-1.5\) | |
Ok, we have determined that the x-intercept is located exactly on the point \((-\frac{3}{2},0)\)
Finding the y-intercept
You will utilize the exact same logic to find the y-intercept. Of course, x will be equal to 0 this time:
| \(4x+5y+6=0\) | Substitute 0 in for x. |
| \(4*0+5y+6=0\) | |
| \(5y+6=0\) | Subtract 6 on both sides. |
| \(5y=-6\) | Divide by 5 on both sides. |
| \(y=-\frac{6}{5}=-1.2\) | |
Ok, we have determined that the y-intercept is located exactly on the point \((0,-1.2)\).
You actually do not need any more information to graph this equation. Plot both the intercepts on a coordinate plane, and use a ruler to connect them. Then, you are done!
+2446 To figure out the equation of a line that passes through the given points (-6, -5) and (-4, -4), you must first know the standard form of a line. It is the following:
\(y=mx+b\)
Let m = slope of the line
Let b = the y-intercept (the point where the line touches the y-axis)
The first step is to figure out the slope of the line. How do we do that, you may ask? All you do is remember the slope formula.
\(m=\frac{y_2-y_1}{x_2-x_1}\)
We already have enough information to calculate the slope, m. We do this by substituting the given points into the formula.
| \(m=\frac{-5-(-4)}{-6-(-4)}\) | Simplify the fraction into simplest terms by evaluating the numerator and denominator separately. |
| \(m=\frac{-5+4}{-6+4}\) | Of course, subtracting a negative is the same as adding a positive. |
| \(m=\frac{-1}{-2}\) | The negatives in the numerator and denominator cancel each other out. |
| \(m=\frac{1}{2}\) | |
Great! We know the slope! Now, the only variable to figure out next is b, the y-intercept. We can do this by plugging in points of points on the line in the equation.
\(y=\frac{1}{2}x+b\)
In other words, to solve for b, you must plug in a point we know is one the line (either (-6,-5) or (-4,-4)) for x and y. I'll choose (-4,-4):
| \(y=\frac{1}{2}x+b\) | Plug in the coordinate (-4,-4) in its appropriate spots and then solve for b. |
| \(-4=\frac{1}{2}*-4+b\) | Now, solve for b. |
| \(-4=-2+b\) | Add 2 on both sides. |
| \(-2=b\) | |
Now that we have solved for both m and b, the equation that passes through the points (-6,-5) and (-4,-4) is \(y=\frac{1}{2}x-2\).
Do you need your answer in point-slope form? No problem! Remember the point-slope form
\(y-y_1=m(x-x_1)\)
Of course, m is the slope again. We have already calculated that. Let's substitute that in.
\(y-y_1=\frac{1}{2}(x-x_1)\)
\(y_1\hspace{1mm}\text{and}\hspace{1mm}x_1\) represent a point on the line. You can either substitute the first or the second set of coordinates. It doesn't matter. However, in the end, your answer should be one of these:
\(y+5=\frac{1}{2}(x+6)\)
\(y+4=\frac{1}{2}(x+4)\)
+2446 I'll be happy to do math that I am assigned! Yay!
To figure this out, we must know the base comparisons. This just requires memorization, unfortunately.
\(1in=0.0254m\)
I happen to know that this is the base comparison. However, I'll have to do 2 conversions. One for the appropriate number of inches and one for meters to millimeters. Here it goes!
| \(\frac{1in}{0.0254m}=\frac{12in}{xm}\) | This is a proportion. Solve by cross multiplying. |
| \(x=12*0.0254=0.3048m\) | Therefore, this shows that 12 inches is equivalent to 0.3048 meters. Now, we must convert to millimeters. |
| \(\frac{1000mm}{1m}=\frac{ymm}{0.3048m}\) | Cross multiply a second time. |
| \(y=0.3048*1000=304.8mm\) | |
Bam! Done! 12 inches = 304.8 millimeters!
+2446 Evaluating inside of parentheses is quite simple, actually. Just remember that if you have multiple operations within a set of parentheses, abide the rules of the order of operations inside of those parentheses.
I'll evaluate your given expression to demonstrate this:
| \(3 (( 2+4)-5)\) | Good! You have identified the set of parentheses from left to right. However, there is an inner set of parentheses. Do that first! Why? |
| \(3(6-5)\) | Yet again, do 6-5 because it is prioritized by the parentheses. |
| \(3(1)\) | 3(1)=3*1. Evaluate this. |
| \(3\) | |
+2446 This is the given info:
\(g(x)=\frac{1}{4}x+\frac{3}{4}\)
\(g(x)=-\frac{3}{2}\)
| \(g(x)=\frac{1}{4}x+\frac{3}{4}\) | To solve for x, substitute -3/2 into the equation for g(x). |
| \(-\frac{3}{2}=\frac{1}{4}x+\frac{3}{4}\) | I will simplify the right hand side of the equation. |
| \(-\frac{3}{2}=\frac{x}{4}+\frac{3}{4}\) | Because x/4 and 3/4 have common denominators, I can add them together. |
| \(\frac{4}{1}*-\frac{3}{2}=\frac{x+3}{4}*\frac{4}{1}\) | To get rid of the pesky fractions, multiply both sides of the equation by the lowest common multiple of all denominators present in the equation. Let's figure out what 4*-3/2 is. |
| \(\frac{4}{1}*-\frac{3}{2}=\frac{4*-3}{2*1}=\frac{-12}{2}=-6\) | Insert this back into the original equation. |
| \(-6=x+3\) | Subtract 3 on both sides. |
| \(-9=x\) | |
+2446 I agree, here, that the language is ambiguous, but you can specify, in words, which interpretation you want.
| Expression | Words |
| \(\pi*7^2\) | What is the product of pi and seven squared? |
| \((\pi*7)^2\) | What is the quantity of pi multiplied by seven all raised to the second power? |
Generally, if you want to indicate parentheses, you will use the term "quantity of..."
