Consider the following equation: − 8 x − 10 y = 19

Question

Consider the following equation: 

A) Write the above equation in the form  Enter the values of  and  in the appropriate boxes below as integers or reduced fractions (in the form A/B.)

Answer:  ____  + _____

B) Use your answer in part (A) to find the ordered pair that lies on this line when 

Answer: (,___) Enter your answer as an integer or a reduced fraction in the form A/B.

Answer 1

Consider the following equation — -8x - 10y = 19

1. This is a linear equation in Standard Form Ax + By = C

A.) Write the above equation in the form y=mx+b. Enter the values of m and b in the appropriate boxes below as integers or reduced fractions

1. Recall the Equality Property of Addition - If a = b, then a + c = b + c
2. -8x - 10y = 19
3. -8x - 10y + 8x = 19 + 8x
4. -10y = 8x + 19
5. Recall the Equality Property of Division - If a = b, then (a/c) = (b/c)
6. -10y = 8x + 19
7. (-10y/-10) = (8x/-10) + (19/-10)
8. (-10/-10)y = (8/-10)x + (19/-10)
9. y = (-4/5)x + (-19/10)
10. Therefore, Slope-Intercept Form y = mx + b of the given linear equation has slope m = (-4/5) and y-intercept at (0, -19/10) with b = (-19/10)

B.) Use your answer in part A to find the ordered pair that lies on this line when x = -40

1. Now we are looking for the corresponding y-value of the given linear equation when x = -40
2. Our equation from part A depends on two unknowns, x and y, however, with a given x-value, we can algebraically solve for the corresponding y-value
3. y = (-4/5)x + (-19/10)
4. y = (-4/5)*(-40) + (-19/10)
5. y = 32 + (-19/10)
6. y = (320/10) - (19/10)
7. y = (301/10)
8. Therefore, the ordered pair solution would be ( -40, 301/10 )