Question

A line and the point (3,4) are graphed in the coordinate plane. what is the equation of the line that passes through the point (3,4) and is parallel to the line shown

A. y= 1/4x+3
B. y=1/4x+13/4
C. y=4x+3
D.y=4x+13/4

Answer 1

B. y=1/4x+13/4

Explanation:

Answer 2

The equation of the line that passes through the point (3,4) and is parallel to the line shown is:

• 
  `y = (1)/(4)x\ +\ (13)/(4)` (option B)

How to obtain the equation of the line?

Step 1: Determine the slope of the line shown in the graph. Details below:

• x₁ = 0
• x₂ = 4
• y₁ = 1
• y₂ = 2
• Slope of line (m₁) =?

`m_1 = (y_2\ -\ y_1)/(x_2\ -\ 1_1)\\\\m_1 = (2\ -\ 1)/(4\ -\ 0)\\\\m_1 = (1)/(4)`

Now, we shall obtain the equation of the parallel to the line shown in the question. Details below:

• Slope of line shown (m₁) =
  `(1)/(4)`
• Slope of the line parallel to the line shown (m₂) = m₁ =
  `(1)/(4)`
• Coordinate of the line = (3, 4)
• x coordinate 1 (x₁) = 3
• y coordinate 1 (y₁) = 4
• Equation of line =?

`y\ -\ y_1 = m_2(x\ -\ x_1)\\\\y\ -\ 4 = (1)/(4) (x\ -\ 3)\\\\y\ -\ 4 = (1)/(4)x\ -\ (3)/(4)\\\\y = (1)/(4)x\ -\ (3)/(4)\ +\ 4\\\\y = (x\ -\ 3\ +\ 16)/(4)\\\\y = (x\ +\ 13)/(4)\\\\y = (1)/(4)x\ +\ (13)/(4)`

Thus, the correct answer is option B