Question

1. the lines below have the same ( x )-intercept. algebraically determine the value of ( k ).

4 points
( 2kx + 4y - 7 = 0 )
( y = (k + 1)x - 4 )

Explanation:

Step1: Find x-intercept of first line

For \(2kx + 4y - 7 = 0\), set \(y = 0\):
\(2kx - 7 = 0 \implies 2kx = 7 \implies x = \frac{7}{2k}\) (assuming \(k
eq 0\)).

Step2: Find x-intercept of second line

For \(y = (k + 1)x - 4\), set \(y = 0\):
\(0 = (k + 1)x - 4 \implies (k + 1)x = 4 \implies x = \frac{4}{k + 1}\) (assuming \(k
eq -1\)).

Step3: Set x-intercepts equal

Since intercepts are equal:
\(\frac{7}{2k} = \frac{4}{k + 1}\)

Step4: Cross-multiply and solve

Cross-multiplying:
\(7(k + 1) = 4(2k)\)
\(7k + 7 = 8k\)
Subtract \(7k\):
\(k = 7\)

Answer:

\(k = 7\)