Question

Octavius wants to write the equation of a line perpendicular to y=-4x+5 that passes through the point 8,-3 . Her work is shown below. Write the equation that she should have written

y + 3 = 4(x − 8)
y + 3 = 4x - 32
y = 4x - 35
y=+x-s

Answer 1

To find the equation of a line perpendicular to y = -4x + 5 and passing through the point (8, -3), Octavius should have written the equation y + 3 = 1/4(x - 8).

Step-by-step explanation:

To find the equation of a line perpendicular to the given line y = -4x + 5 and passing through the point (8, -3), we need to determine the slope of the perpendicular line. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. The given line has a slope of -4, so the perpendicular line will have a slope of 1/4.

Using the slope-intercept form, we can write the equation as y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Plugging in the values, we get y - (-3) = 1/4(x - 8). Simplifying this equation, we have y + 3 = 1/4(x - 8). Therefore, the correct equation that Octavius should have written is y + 3 = 1/4(x - 8).