1. Explain how to find the slope of a line from a table of data.
A: ?
2. Explain how to justify the Cross Products Property by using Mulitplication Property of Equality.
A: ?
Let's say this is your table:
x y
0 1
1 3
2 5
Plot those points on a graph. Now, notice when you move on the x number line from 1 to 2 you're moving up 2 spaces. That means your slope is 2 and when x = 0, what does y=? That's your intercept.
So, the standard form of that table would be y = 2x+1 or y=slope times x plus the intercept.
Hope that helps.
In answer to the other question, first we need to know:
The Multiplication Property of Equality states that if you multiply both sides of an equation by the same number, the sides remain equal (i.e. equality is preserved).
and
Cross Product Property states that in a proportion, product of the means is equal to the product of the extremes.
So, per the Cross Product property:
A = C
B D
Now, multiply both sides by B. You get AB over B which is A and CD over D. So now you have A=CB/D
Now multiply both sides by D. You get AD = CBD over D which is the same as AD = CB.
Ta-dah!
1. To find the slope of a line from a table of data, you need to identify two points on the line. Let's call these points (x1, y1) and (x2, y2), where x1 and x2 are the x-coordinates and y1 and y2 are the y-coordinates.
Once you have identified these points, you can use the slope formula:
slope = (y2 - y1) / (x2 - x1).
Substitute the values of y2, y1, x2, and x1 from the table into the slope formula. Calculate the difference in the y-values and the difference in the x-values, and divide them to find the slope of the line.
2. The Cross Products Property states that if two ratios are equal, then their cross products are equal. Let's take an example to understand this property better:
Suppose we have two ratios, a/b and c/d, where a, b, c, and d are numbers. According to the Cross Products Property, if a/b = c/d, then ad = bc.
To justify the Cross Products Property using the Multiplication Property of Equality, we can start with the assumption that a/b = c/d.
Now, we want to show that ad = bc. We can do this by multiplying both sides of the equation a/b = c/d by bd (the product of the denominators).
(a/b) * bd = (c/d) * bd
Multiplying both sides of the equation by bd does not change the equality, following the Multiplication Property of Equality.
On the left-hand side, the b in the numerator and the b in the denominator cancel out, leaving us with a * d.
On the right-hand side, we have c * bd / d, and similarly, the d in the numerator and the d in the denominator cancel out, leaving us with c * b.
Therefore, we have ad = bc, which justifies the Cross Products Property using the Multiplication Property of Equality.