Final answer:
The correct equation for Penny's line, which is perpendicular to Albert's line represented by y = -1/2x + 5 and passes through the point (-4,3), is y = 2x + 11. This is found by taking the negative reciprocal of the original line's slope and using the point-slope formula.
Step-by-step explanation:
The student is asking about the equation of a line that is perpendicular to an existing line and passes through a specific point on a coordinate plane. To solve this, we must understand the concept of slope and how it affects the orientation of lines in relation to one another. The slope is a measure of how steep a line is and is represented by the m in the line equation y = mx + b, where b is the y-intercept.
Albert's line has an equation y = -1/2x + 5. Since the slope of Albert's line is -1/2, the slope of a line perpendicular to it will be the negative reciprocal, which is 2. Penny's line passes through the point (-4,3), so using the point-slope form of the line equation, y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope, we can find Penny's line equation.
Substitute the point (-4,3) and the slope 2 into the point-slope equation to get y - 3 = 2(x + 4). Simplifying this, we get y = 2x + 11. Therefore, the correct equation that represents Penny's line is y = 2x + 11, which means Option B is the correct choice, assuming the correct format of Option B should be y = 2x +11.