Question

question 1 of 10
which point lies on the line described by the equation below?
y + 4 = 4(x - 3)

a. (1, 11)
b. (2, 9)
c. (0, 0)
d. (3, -4)
e. (-2, 3)
f. (1, -11)

Explanation:

Step1: Recall the point - line relationship

A point \((x,y)\) lies on the line defined by the equation \(y + 4=4(x - 3)\) if and only if when we substitute the \(x\) - coordinate and \(y\) - coordinate of the point into the equation, the equation holds true (i.e., the left - hand side is equal to the right - hand side).

Step2: Test option A \((1,11)\)

Substitute \(x = 1\) and \(y = 11\) into the left - hand side (LHS) and right - hand side (RHS) of the equation \(y + 4=4(x - 3)\).

• LHS: \(y+4=11 + 4=15\)
• RHS: \(4(x - 3)=4\times(1 - 3)=4\times(-2)=-8\)

Since \(15
eq - 8\), the point \((1,11)\) does not lie on the line.

Step3: Test option B \((2,9)\)

Substitute \(x = 2\) and \(y = 9\) into the equation.

• LHS: \(y + 4=9+4 = 13\)
• RHS: \(4(x - 3)=4\times(2 - 3)=4\times(-1)=-4\)

Since \(13
eq - 4\), the point \((2,9)\) does not lie on the line.

Step4: Test option C \((0,0)\)

Substitute \(x = 0\) and \(y = 0\) into the equation.

• LHS: \(y + 4=0 + 4=4\)
• RHS: \(4(x - 3)=4\times(0 - 3)=4\times(-3)=-12\)

Since \(4
eq - 12\), the point \((0,0)\) does not lie on the line.

Step5: Test option D \((3,-4)\)

Substitute \(x = 3\) and \(y=-4\) into the equation.

• LHS: \(y + 4=-4 + 4=0\)
• RHS: \(4(x - 3)=4\times(3 - 3)=4\times0 = 0\)

Since LHS = RHS (\(0 = 0\)), the point \((3,-4)\) lies on the line.

Step6: Test option E \((-2,3)\) (for completeness)

Substitute \(x=-2\) and \(y = 3\) into the equation.

• LHS: \(y + 4=3+4 = 7\)
• RHS: \(4(x - 3)=4\times(-2 - 3)=4\times(-5)=-20\)

Since \(7
eq - 20\), the point \((-2,3)\) does not lie on the line.

Step7: Test option F \((1,-11)\) (for completeness)

Substitute \(x = 1\) and \(y=-11\) into the equation.

• LHS: \(y + 4=-11 + 4=-7\)
• RHS: \(4(x - 3)=4\times(1 - 3)=4\times(-2)=-8\)

Since \(-7
eq - 8\), the point \((1,-11)\) does not lie on the line.

Answer:

D. (3, -4)