4. Line r is mapped onto line m by a dilation centered at the origin with a scale factor of 4. The equation of line r is 6x – 3y = 12. What is the
equation for line m?

3x - y = 8

Step-by-step explanation:

Since, if a line having points represented by (x,y) is dilated about origin with a scale factor k,

Then the coordinates of the dilated line is obtained by the rule,

Here, line L is,

3x - y = 4

The x-intercept and y-intercept of line L are (4/3,0) and (0,-4) respectively,

If the line L is mapped onto line M by a dilation centered at the origin with a scale factor of 2,

Then by the above definition,

The points of the line M are,

(2×4/3, 2×0) and (2×0, 2×-4) ⇒ (8/3,0) and (0,-8)

Hence, the equation of line M passes through the points (8/3,0) and (0,-8)

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)