First, we must find the equation of the given line. The slope is "rise over run," or the change in y over the change in x from one point to another. The two points shown are (0,-1) and (3,1). In these points, y increases by 2. This means the change in y is 2. In these points, x increase by 3. This means the change in x is 3. Thus, the change in y over change in x is 2/3. This means that the slop of the given line is 2/3.
In the form y=mx+b, where m is the slope, b is the y intercept. This is because the y intercept occurs when x is 0. If x is zero, mx is zero, so y=b. In other words, when x equals 0, y=b. This creates the point (0,b), which is the y-intercept. Since the y-intercept of the given line is -3, the equation for this line is: y=2/3x-3.
A line parallel to this will need to have the same slope. This allows us to eliminate choices C and D, which do not have the same slope.
In order for the line to have an x-intercept of (-3,0), y must equal 0 when x is -3, since ordered pairs are (x,y). We can solve the equation using the information we know: 0=((2/3)(-3))+b This is because we know the slope is 2/3, and that when x is -3, y is 0.
Then, we can solve from there: 0=(-2)+b (just multiply 2/3 and -3) 2=b (add 2 to both sides)
One simple way to approach this is to subtract the number that DOESN’T have the variable with the solution by the sum. Lets use problem 1 as the example: 1.) N+8=13 In this case, we subtract 13 by 8 and get 5, therefore N= 5.
2.) B+17=62 62-17= 45 B= 45
3.) X+5/6= 7/16 7/16-5/6= -19/48 X= -19/48
4.) y+1/7=5/8 5/8-1/7= 27/56 Y= 27/56
5.) 14+y=69 69-14=55 Y=55
6.) c+3.6=4.9 4.9-3.6=1.3 C= 1.3
Now for the word problems: Lets use 7 as the example- 7.) a number increased by 19 is equal to 221. Since we don’t know the number being increased by 19, that will be our variable. It will be re-written as so:
N + 19 = 221
Where N is the unknown number.
Using the same method of subtracting by the sum and the number that’s not the variable, we’ll get the solution to N 221-19= 202 N= 202
