Final answer:
To write an equation in slope-intercept form for a line perpendicular to y = -4x - 5, we find the slope of the given line and then find the negative reciprocal to obtain the slope of the new line. We then use the point-slope form of a line, y - y1 = m(x - x1), and plug in the values to find the equation in slope-intercept form.
Step-by-step explanation:
To write an equation in slope-intercept form for a line that is perpendicular to another line, we first need to determine the slope of the given line. The given line has the equation y = -4x - 5, which can be rewritten in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -4.
Since the line we want to find is perpendicular to the given line, its slope will be the negative reciprocal of -4. So, the slope of the line we want to find is 1/4.
Now that we have the slope and the point through which the line passes (P(2, -3)), we can use the point-slope form of a line to find the equation. The point-slope form is y - y1 = m(x - x1). Plugging in the values, we get y - (-3) = 1/4(x - 2), which simplifies to y + 3 = 1/4x - 1/2. Rearranging the equation to slope-intercept form, we get y = 1/4x - 1/2 - 3, which can be simplified to y = 1/4x - 7/2.