Question

slopes of non - parallel lines. the graph shows four linear functions. ( l(x)=2x ), ( g(x)=2x - 10 ), ( k(x)=-\frac{2}{3}x ), ( h(x)=\frac{2}{3}x+10 ). study the linear functions graphed to complete each statement. consider the two lines represented by the functions ( h(x)=-\frac{2}{3}x ) and ( j(x)=\frac{2}{3}x + 10 ). to determine where the lines intersect, you can set both functions equal to each other and solve. the equation ( -\frac{2}{3}x=\frac{2}{3}x + 10 ). this means that the two lines described by the functions ( h(x)=-\frac{2}{3}x ) and ( j(x)=\frac{2}{3}x + 10 ). what patterns have you noticed? the slopes of parallel lines are

Explanation:

Step1: Set the two functions equal

\[-\frac{2}{3}x=\frac{2}{3}x + 10\]

Step2: Move \(x\) - terms to one side

Add \(\frac{2}{3}x\) to both sides:
\[0=\frac{2}{3}x+\frac{2}{3}x + 10\]
\[0=\frac{4}{3}x+10\]

Step3: Isolate \(x\)

Subtract 10 from both sides:
\[- 10=\frac{4}{3}x\]
Multiply both sides by \(\frac{3}{4}\):
\[x=-10\times\frac{3}{4}=-\frac{30}{4}=-\frac{15}{2}=- 7.5\]

Answer:

\(x = - 7.5\)