What is the equation of a line that is perpendicular to the given line and has an x-intercept of 6?

y = 4/3(x) - 8

Step-by-step explanation:

First we have to find the equation for the given line (I use y = mx + b for everything, although I think it can be done with other formats). The equation for slope is (y2 - y1)/(x2 - x1) = m, so we'll start with that.

(-2 - 4) / (4 - (-4)) = m

-6 / 8 = m

m = -3/4

Now, let's find the rest of the equation. We can do this by treating b as the unknown variable it is, and plugging in a known xy pair, then simply solving for the unknown variable.

y = mx + b; y = 4, x = -4, m = -3/4

4 = -4(-3/4) + b

4 = 3 + b

b = 1

Now we have the original line's equation, y = -3/4(x) + 1. We need to find the new line's slope by finding the negative reciprocal of the base line's. For that, we simply flip the numerator and denominator, then multiply it by -1, to get 4/3. Now we find b again, using the point (6, 0).

y = mx + b; y = 0, x = 6, m = 4/3

0 = 4/3(6) + b

0 = 8 + b

b = -8

This makes our final answer y = 4/3(x) - 8.

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3