Question

Write an equation
that goes through
(8.1) and is
perpendicular to 2y
+4x =12

Answer 1

To find the equation of a line that goes through a given point and is perpendicular to a given line, we can use the following steps:

Rewrite the given line in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

Determine the slope of the line that is perpendicular to the given line. The slope of a line perpendicular to a line with slope m is -1/m.

Use the point-slope form of the equation of a line to write the equation of the line that goes through the given point with the slope found in step 2.

Given the point (8, 1) and the line 2y + 4x = 12, we can rewrite the line in slope-intercept form by solving for y:

2y + 4x = 12

2y = -4x + 12

y = -2x + 6

The slope of the given line is -2.

The slope of the line perpendicular to the given line is -1/-2 = 1/2.

Using the point-slope form of the equation of a line, we can write the equation of the line that goes through the point (8, 1) with slope 1/2:

y - 1 = (1/2)(x - 8)

Simplifying this equation, we get:

y - 1 = (1/2)x - 4

y = (1/2)x - 3

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

Explanation:

Answer 2

To find an equation that goes through the point (8.1) and is perpendicular to 2y + 4x = 12, we can first rearrange the given equation into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept:

2y + 4x = 12

2y = -4x + 12

y = -2x + 6

So the slope of the given equation is -2.

Since we want a line that is perpendicular to this line and passes through the point (8,1), we know that the slope of our new line will be the negative reciprocal of -2, which is 1/2.

Now we can use the point-slope form of the equation of a line to write the equation:

y - 1 = (1/2)(x - 8)

Simplifying this equation, we get:

y - 1 = (1/2)x - 4

y = (1/2)x - 3

Therefore, the equation that goes through the point (8,1) and is perpendicular to 2y + 4x = 12 is y = (1/2)x - 3.