Question

complete the following equations. enter an equation for line f: y = 2x line v is a translation of line f. enter an equation for line v: y = x+( )

Explanation:

Step1: Recall slope - intercept form

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For two parallel lines (a translation is a parallel - shift), the slopes are equal. Given \(y = 2x\) for line \(f\), the slope of line \(v\) is also \(m = 2\).

Step2: Use a point on line \(v\) to find \(b\)

Let's assume we can identify a point \((x_0,y_0)\) on line \(v\) from the graph. Suppose the point \((- 4,-4)\) lies on line \(v\). Substitute \(x=-4\), \(y = - 4\) and \(m = 2\) into \(y=mx + b\). We get \(-4=2\times(-4)+b\).

Step3: Solve for \(b\)

First, simplify the right - hand side: \(2\times(-4)=-8\). So the equation becomes \(-4=-8 + b\). Add 8 to both sides of the equation: \(b=-4 + 8=4\).

Answer:

\(y=2x + 4\)