Final answer:
To find the equation of the line passing through (-7, -2) and parallel to Y = 2x + 1, use the slope of 2 and apply the point-slope form to get y = 2x + 12 in slope-intercept form.
Step-by-step explanation:
The question asks us to find the equation of a line passing through the point (-7, -2) which is parallel to the line with equation Y = 2x + 1. Since parallel lines have the same slope, the slope of our new line will also be 2 (the coefficient of x in the given equation). The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
To find the y-intercept of our new line, we use the point (-7, -2) and the slope 2 in the point-slope form of the linear equation, which is y - y1 = m(x - x1). Plugging in our values gives us y - (-2) = 2(x - (-7)) or y + 2 = 2(x + 7). Simplifying further, y + 2 = 2x + 14. Subtracting 2 from both sides to get y alone on one side gives us the equation y = 2x + 12. This is the equation of our line in slope-intercept form with the y-intercept as 12.