Question 8 (1 point) \( \begin{array}{l}\text { (04.02 MC) } \\ \text { The equation of line EF is } y=2 x+1 \text {. Write an equation of a line parallel to line EF in slope-intercept form that contains point }(0,2) \\ \text { a } \quad y=2 x-4 \\ \text { c } \quad y=2 x+2 \\ \text { d } \quad y=-\frac{1}{2} x-4 \\ y=\frac{-1}{2} x+2\end{array} \)

To find an equation of a line parallel to line EF, we know that parallel lines have the same slope. The slope of line EF, given by the equation \(y = 2x + 1\), is 2. Now, we need to find the y-intercept for the parallel line that passes through point (0, 2). Using the point-slope form, we can determine the new line’s equation: 1. The equation will still have the same slope: 2. 2. Since the line passes through (0, 2), we can directly deduce its equation as \(y = 2x + 2\). So, the correct answer is \(c \quad y = 2x + 2\). A fun fact: Did you know that slopes in parallel lines represent not just a relationship in geometry but also in the context of real-life roads and paths? When two roads run parallel, they maintain the same steepness – just like our lines on a graph! As for the concept of slope in art, imagine how artists use lines and angles in their drawings and paintings. Lines with different slopes can create visual interest and depth, while parallel lines can give a sense of harmony and balance. Pretty cool, right?