Doing something wrong. Write an equation of the line containing the given point and perpendicular to the given line. (4,5;)4x+y=8; I tried this.

y = -4x+8. The slope is the reciprocal of -4 so 1/4. Then (y - y^1=m(x-x^1).
y -4 = 1/4(x-4). I then multiplied 1/4 and 4 then added -4 to both sides but still managed to get a wrong answer of 1/4x +5???

I agree that your line is of the form

y = (1/4)x + b

5 = 1 + b
b = 4

y = (x/4) + 4

Ok,I was one off. Thank you!!!

To find the equation of a line that is perpendicular to the given line, you need to determine the slope of the given line and then find the negative reciprocal of that slope.

Given line: 4x + y = 8

First, let's rearrange the equation in slope-intercept form (y = mx + b) by subtracting 4x from both sides:
y = -4x + 8

From this equation, we can see that the slope of the given line is -4.

To find the slope of the line perpendicular to it, we take the negative reciprocal of the slope -4. The negative reciprocal is found by taking the negative of the reciprocal of the slope. In this case, the reciprocal of -4 is -1/4, and the negative of that would be 1/4.

So, the slope of the line perpendicular to the given line is 1/4.

Now that we have the slope, we can use the point (4, 5) that the line passes through to write the equation using the point-slope form:

y - y1 = m(x - x1)

Substituting the values, we have:
y - 5 = 1/4(x - 4)

Now you need to simplify the equation. Distribute 1/4 to (x - 4):
y - 5 = 1/4x - 1

To isolate y, add 5 to both sides of the equation:
y = 1/4x + 4

Therefore, the equation of the line that passes through the point (4, 5) and is perpendicular to the line 4x + y = 8 is y = 1/4x + 4.

It seems like you made a calculation error when multiplying 1/4 and 4. When you multiply 1/4 and 4, you should get 1, not 1/4 as you stated. Double-check your calculations to avoid such errors.