Question

The equation of line p is y=ax+b. Which of these could be the equation of line q? A.y=−3a(x+6)+b

B.y=−3ax+b+6
C.y=3a(x+6)+b
D.y=3ax+b−

Answer 1

Equation of line q: y=3ax+b-6

D is correct.

Explanation:

The equation of line p is y=ax+b

Blue line is the graph of line p.

In graph we can see slope is positive and y-intercept (0,5)

So, a>0 and b=5

Passing point of p is (-2,1)

We can find the value of a also

`1=-2a+5`

`a=2`

The equation of line p: y=2x+5 ( Blue Line)

Now, we find the equation of line q using blue line.

The slope of line q is positive and greater than 2

Possible options are C and D because A and B are negative slope.

y-intercept of red line is (0,-1)

y-intercept of p (0,5)

y-intercept of q (0,-1)

If we shift 6 unit down of line p to get line q

y=3ax+b-6 (Red line)

Hence, The equation of line q is y=3ax+b-6

Answer 2

The slope of line q is that of line p scaled by a factor of 3 (not -3). The y-intercept of line q is 6 less than the y-intercept of line p. The appropriate choice is
D. y = 3ax +b -6