Final answer:
To write the equation of a line passing through (-5, 2) and parallel to the line y = -4x +3, substitute the values of (-5, 2) and -4 into the point-slope form equation. Simplify the equation and the result is y = -4x - 18.
Step-by-step explanation:
To write the equation of a line passing through (-5, 2) and parallel to the line y = -4x +3, we need to determine the slope of the given line. The slope of a line is represented by the coefficient of x in its equation. In this case, the given line has a slope of -4. Since two parallel lines have the same slope, the slope of the line we are trying to find is also -4.
Using the point-slope form of the equation of a line, y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can substitute the values of (-5, 2) and -4 into the equation. This gives us y - 2 = -4(x + 5).
Simplifying the equation, we get y - 2 = -4x - 20. Finally, adding 2 to both sides of the equation, we have y = -4x - 18. Therefore, the equation of the line passing through (-5, 2) and parallel to y = -4x + 3 is y = -4x - 18.