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,
[tex]9x+3y=18[/tex]
[tex]9x+3y-9x=18-9x[/tex]
[tex]\text{ 3y = 18 - 9x}[/tex]
[tex]\text{ }\frac{\text{3y}}{3}\text{ = }\frac{\text{18 - 9x}}{3}[/tex]
[tex]\text{ y = 6 - 3x}[/tex]
[tex]\text{ y =-3x + 6}[/tex]
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:
[tex]\text{ y =-3x + 6}[/tex]
The answer to question 15 is:
[tex]y=\frac{1}{3}x-9[/tex]
