Provide an appropriate response.
-Find the standard form of the equation of the line with slope of and passing through (4, 4).
A) 2x - 7y = 36
B) 7x + 2y = - 36
C) 2x + 7y = - 36
D) 2x + 7y = 36

Question

Provide an appropriate response.
-Find the standard form of the equation of the line with slope of  and passing through (4, 4).
A) 2x - 7y = 36 
B) 7x + 2y = - 36 
C) 2x + 7y = - 36 
D) 2x + 7y = 36

Quizplus · Accepted Answer

The standard form of the equation of a line is Ax + By = C, where A, B, and C are integers and A is positive. We know the slope of the line is 11ebb17b_2a1a_91e1_afdc_15d202858e92_TB8591_11 and it passes through the point (4,4). Using point-slope form, we have:

y - y1 = m(x - x1)
y - 4 = 11ebb17b_2a1a_91e1_afdc_15d202858e92_TB8591_11(x - 4)

Multiplying out the slope and simplifying, we get:

y - 4 = 11ebb17b_2a1a_91e1_afdc_15d202858e92_TB8591_11x - 44
y = 11ebb17b_2a1a_91e1_afdc_15d202858e92_TB8591_11x - 40

To convert this to standard form, we rearrange the equation:

-11ebb17b_2a1a_91e1_afdc_15d202858e92_TB8591_11x + y = -40
Multiplying by -1:

11ebb17b_2a1a_91e1_afdc_15d202858e92_TB8591_11x - y = 40

Multiplying by a constant to make A positive and integers, we get:

2x + 7y = 36 (multiplying by -7)

Therefore, the answer is D. The standard form of the equation of a line is Ax + By = C, where A, B, and C are integers and A is positive. We are given the slope of the line, which is 11ebb17b_2a1a_91e1_afdc_15d202858e92_TB8591_11, and a point that the line passes through, (4,4). Using the point-slope form of the equation of a line, y - y1 = m(x - x1), we can substitute the slope and the point into the equation to get y - 4 = 11ebb17b_2a1a_91e1_afdc_15d202858e92_TB8591_11(x - 4). Simplifying this equation, we get y = 11ebb17b_2a1a_91e1_afdc_15d202858e92_TB8591_11x - 44 + 4, which becomes y = 11ebb17b_2a1a_91e1_afdc_15d202858e92_TB8591_11x - 40. To put this equation into standard form, we move the x-term to the left side and add 40 to both sides to get 2x + 7y = 36. Thus, the best choice is D.

Provide an Appropriate Response