Question

Convert the standard equation 9x + 3y =18 to slop intercept form.Covert the point slope equation y= 1/3 (x-3) -8 to slop-intercept form.

Answer 1

14.) Convert the standard equation 9x + 3y = 18 to slope-intercept form.

Converting the given equation into standard form means we will be transforming the given equation into the following form: y = mx + b.

We get,

`9x+3y=18`

`9x+3y-9x=18-9x`

`\text{ 3y = 18 - 9x}`

`\text{ }\frac{\text{3y}}{3}\text{ = }\frac{\text{18 - 9x}}{3}`

`\text{ y = 6 - 3x}`

`\text{ y =-3x + 6}`

Therefore, the slope-intercept form of the equation 9x + 3y = 18 is y = -3x + 6.

15.) Covert the point slope equation y = 1/3 (x-3) - 8 to slope-intercept form.

From the point-slope equation y = 1/3 (x-3) - 8,

y = 1/3 (x-3) - 8

(y + 8) = 1/3(x - 3)

We get,

Slope = m = 1/3

x₁ = 3

y₁ = -8

To convert it to a slope-intercept form, let's first find the y-intercept (b).

Substitute m = 1/3 and x,y = 3, -8 in y = mx + b.

y = mx + b

-8 = 1/3(3) + b

-8 = 1 + b

-8 - 1 = 1 + b - 1

-9 = b

b = -9

Let's now complete the equation, substitute m = 1/3 and b = -9 in y = mx + b.

y = mx + b

y = (1/3)x + (-9)

y = 1/3(x) - 9

In summary,

The answer to question 14 is:

`\text{ y =-3x + 6}`

The answer to question 15 is:

`y=(1)/(3)x-9`