Final Answer:
The equation of the line using the point-slope formula that has a slope of 1/3 and passes through the point (-3, 9) is y = (1/3)x + 10.
Step-by-step explanation:
Let's find the equation of the line using the point-slope formula, given that it has a slope (m) of 1/3 and passes through the point (-3, 9).
The point-slope form of the line is given by the equation:
y - y₁ = m(x - x₁)
where m is the slope of the line and (x₁, y₁) is a point on the line.
Substituting the given values into the point-slope form, we get:
y - 9 = 1/3(x - (-3))
Now, let's simplify the equation:
y - 9 = 1/3(x + 3)
Distributing the slope 1/3 across the terms in the parenthesis:
y - 9 = (1/3)x + (1/3)*(3)
Simplify the constant term on the right side:
y - 9 = (1/3)x + 1
Now let's isolate y by adding 0 to both sides of the equation:
y = (1/3)x + 1 + 9
Combine the constant terms on the right:
y = (1/3)x + 10
So the equation of the line in slope-intercept form (y = mx + b) is:
y = (1/3)x + 10
And that is the equation of the line with a slope of 1/3 passing through the point (-3, 9).