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What is the equation of the line using the point-slope formula that has a slope of 1/3 and passes through the point (-3, 9)?

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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).

User Jublikon
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