Final answer:
Line B, being parallel to line A (with equation y = 2/5x + 2), shares the same slope of 2/5 and passes through the point (-5, 2). By substituting the point into the slope-intercept form equation, the y-intercept (b) is found to be 4. Thus, the equation of line B is y = 2/5x + 4.
Step-by-step explanation:
The subject of the question is determining the equation of a line (line B) that is parallel to a given line (line A) with equation y = 2/5x + 2, given that line B passes through the point (-5,2).
Since line A and line B are parallel, they have the same slope. The slope of line A is given as 2/5, so the slope of line B must also be 2/5. To find the equation of line B, we use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. Plugging in the slope and the point (-5,2) into the equation, we solve for b:
y = mx + b
2 = (2/5)(-5) + b
2 = -2 + b
b = 4
Therefore, the equation of line B in slope-intercept form is y = 2/5x + 4.