Question 1
How do you find the y-intercept for 3x – 8y = 48?
The y-intercept of a graph is the point at which the graph crosses the y-axis. For linera equations this is a a single point that can be discerned by examining an equation in the slope-intercept form of y=mx+by=mx+b where b is the y-intercept.
Question 2
The path of a train A is given by the equation 3x + 4y – 12 = 0 and the path of another train B is given by the equation 6x + 8y – 48 = 0. Represent this situation graphically.
In reference to a linear line, the basic representation of it is y=ax+by=ax+b. The coefficient of xx in the equation is termed as the slope of the line. The slope is rate of change of the dependent variable with the change in the independent variable. The y-intercept is bb.
Question 3
Boyle Manufacturing Co. charges factory overhead to production at 80% of direct labor cost. Jobs 842 and 843 were completed and sold in July, 20B. Total direct materials cost and prime cost for Job 842 were P9,000 and P14,000, respectively. Production cost of Job 843 amounted to P31,200 with factory overhead equal to 48% of direct materials cost. How much were the direct labor costs of Job and 843?
Answer to question 1
The y-intercept is -6.
To find the y-intercept we rearrange this equation so that it is in slope-intercept form. This is done by subtracting 3x from both sides and then dividing the entire equation by -8 in order to isolate y.
Answer to question 2
Given Data
- The path of train A is: A=3x+4y−12=0A=3x+4y−12=0.
- The path of train B is: B=6x+8y−48=0B=6x+8y−48=0.
The path of train A can be further simplified as:
34x+y−3=0y=−34x+334x+y−3=0y=−34x+3
The slope of the path of train A is mA=−34mA=−34 and y-intercept is 33.
The path of train B can be further simplified as:
34x+y−6=0y=−34x+634x+y−6=0y=−34x+6
The slope of the path of train B is mB=−34mB=−34 and y-intercept is 66.
Slope of both the trains are same. Both the linear lines on the graph will be parallel.
The graphical representation of both the paths is given below:
Answer to question 3
Step 1
Prime cost comprises of direct material and direct labor
Step 2
For Job 842
Direct materials=9000
Prime cost=14000
So, direct labor=14000-9000=5000
Step 3
For job 843,
Material cost=x
Labor cost=y
X+y+0.48x=31200
X+y+0.8y=31200
0.48x=0.8y
So, x=0.8/.48y
0.8/0.48y+y+0.8y=31200
Or, 0.8y+0.48y+0.384y=31200×0.48
Or, 1.664y=14976
Or y=9000
X=0.8/.48×9000=15000
So, direct labour=$9000