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

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

• A. y = 2x + 1
• B. y = 2x + 2
• C. y = 2x + 3
• D. y = 2x + 4

Answer: (B)

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 =

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 =