Find the equation of a line that passes through the point (1, 2) and has a slope of 1/3. Show how you found the equation.
To find the equation of a line that passes through the point (1, 2) and has a slope of 1/3, we can use the point-slope form of a linear equation.
The point-slope form of a linear equation is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) represents a point on the line and m represents the slope.
In this case, (x₁, y₁) = (1, 2) and m = 1/3. Substituting these values into the point-slope form, we get:
y - 2 = 1/3(x - 1)
Next, we can simplify the equation. Distribute 1/3 to both terms inside the parentheses:
y - 2 = 1/3x - 1/3
To get rid of the fraction, we can multiply both sides of the equation by 3:
3(y - 2) = 3(1/3x - 1/3)
3y - 6 = x - 1
Finally, we can rearrange the equation so that it is in the form y = mx + b (slope-intercept form):
3y = x - 1 + 6
3y = x + 5
y = (1/3)x + 5/3
Therefore, the equation of the line that passes through the point (1, 2) and has a slope of 1/3 is y = (1/3)x + 5/3.