If a linear equation has a slope of 2 and passes through the point (1, 3), what is the equation of the line?

To determine the equation of the line given a slope of 2 and a point (1, 3), we can use the point-slope form of a linear equation, which is expressed as (y - y_1 = m(x - x_1)). Here, (m) represents the slope, and ((x_1, y_1)) represents the coordinates of the point the line passes through.

Substituting the given values into the point-slope form, we have:

• (m = 2)

• (x_1 = 1)

• (y_1 = 3)

Plugging these into the equation gives:

[

y - 3 = 2(x - 1)

]

Now, we can simplify this equation. Distributing the slope on the right side:

[

y - 3 = 2x - 2

]

Next, add 3 to both sides to isolate (y):

[

y = 2x - 2 + 3

]

This simplifies further to:

[

y = 2x + 1

]

Thus, the correct equation of the line is (y =