Question

Write an equation of the line that passes through (8,1) and is perpendicular to the line 2y+4x=12.

Answer 1

The equation of the line that passes through (8,1) and is perpendicular to the line 2y + 4x = 12 is y = 1/2x - 3.

Step-by-step explanation:

To write an equation of a line that is perpendicular to another, you need to find the negative reciprocal of the original line's slope. First, let's get the slope of the given line 2y + 4x = 12. We can rewrite it in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

By rearranging the equation 2y + 4x = 12, we have:
2y = -4x + 12
y = (-4/2)x + (12/2)
y = -2x + 6

The slope of the given line is -2. The slope of a line perpendicular to this will be the negative reciprocal, so m = 1/2. Now, using the point (8,1) that the new line passes through, we can use the point-slope form: y - y1 = m(x - x1), where (x₁, y₁) is a point on the line.

Here, x₁ = 8 and y₁ = 1, so we have:
y - 1 = 1/2(x - 8)

To write this in slope-intercept form, we distribute and rearrange:
y - 1 = 1/2x - 4
y = 1/2x - 3

This is the equation of the line that passes through (8,1) and is perpendicular to the line 2y + 4x = 12.

Answer 2

y=1/2x-3

Step-by-step explanation:

To solve for the slope of this equation, we have to find the negative reciprocal of the slope of 2y+4x=12.

To solve for the slope of 2y+4x=12, we do -a/b, which is -4/2, which simplifies to -2.

From here, we get the negative reciprocal of -2, which is 1/2. This is the slope for the new equation.

The y-intercept is -3.

Now we can substitute the values into the equation to get an answer of:

y=1/2(slope)x - 3(y-intercept)

Hope this helps! :)