Write the equation of the line perpendicular to 2x+8y=16 passing through (4,-2) in slope intercept form.
y+2 = 4(x-4)
now rearrange to the right form
m1 = -A/B = -2/8 = -1/4
m2 = -(-4) = 4
Y = m2x+b
-2 = 4*4+b
b = -18
Y = 4x-18.
To find the equation of the line perpendicular to 2x + 8y = 16, we need to determine the slope of the given line. We can rewrite the equation in slope-intercept form, y = mx + b, where m represents the slope:
2x + 8y = 16
8y = -2x + 16
y = (-2/8)x + 2
y = (-1/4)x + 2
The slope of the given line is -1/4.
For a line to be perpendicular to this line, the slopes must be negative reciprocals of each other. So, the slope of the perpendicular line will be the reciprocal of -1/4, which is 4.
We also have a point through which the perpendicular line passes, which is (4,-2).
Using the point-slope form, y - y1 = m(x - x1), where (x1, y1) are the coordinates of the given point, we can substitute in the values to get the equation:
y - (-2) = 4(x - 4)
y + 2 = 4x - 16
y = 4x - 18
Therefore, the equation of the line perpendicular to 2x + 8y = 16 passing through (4,-2) in slope-intercept form is y = 4x - 18.
To find the equation of the line perpendicular to 2x + 8y = 16, we need to find the slope of the given line and then determine the slope of the perpendicular line.
Step 1: Convert the given equation to slope-intercept form (y = mx + b).
2x + 8y = 16
8y = -2x + 16
y = (-2/8)x + 2
y = (-1/4)x + 2
Step 2: Identify the slope of the given line.
The slope-intercept form is y = mx + b, where m represents the slope. So, the slope of the given line is (-1/4).
Step 3: Determine the slope of the line perpendicular to the given line.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. In this case, the slope of the perpendicular line will be the negative reciprocal of (-1/4).
Reciprocal: Flip the fraction: (-1/4) → (-4/1)
Negative: Change the sign: (-4/1) → 4/1
So, the slope of the line perpendicular to 2x + 8y = 16 is 4/1 or simply 4.
Step 4: Use the slope-intercept form (y = mx + b) and the given point (4, -2) to find the equation of the perpendicular line.
y = mx + b
y = 4x + b
Now, substitute the coordinates (4, -2) into the equation:
-2 = 4(4) + b
-2 = 16 + b
b = -18
Finally, substitute the value of b into the equation, and we have:
y = 4x - 18
Therefore, the equation of the line perpendicular to 2x + 8y = 16 passing through the point (4, -2) in slope-intercept form is y = 4x - 18.