Answer :

olumideolawoyin

Answer:

y = x/2

Step-by-step explanation:

Let (x1, y1) = (4, 2).

[tex]slope \: = \frac{y - y_{1}}{x - x_{1} } [/tex]

[tex] \frac{1}{2} = \frac{y - 2}{x - 4} [/tex]

2(y - 2) = x - 4 Open the brackets

2y - 4 = x - 4 Add +4 to both sides

2y = x - 4 + 4

2y = x + 0 Divide both sides by 2

y = x/2

Teamce170

• Answer:

[tex] \Large{\boxed{\sf y = \dfrac{1}{2}x}} [/tex]

[tex] \\ [/tex]

• Explanation:

We know that the equation of a line in slope-intercept form is:

[tex] \Large{\left[ \begin{array}{c c c} \underline{\tt Slope-Intercept \ Form \text{:}} \\ ~ \\ \tt y = mx + b \end{array} \right] } [/tex]

Where:

• (x , y) is a point on the line.

• m is the slope of the line.

• b is the y-intercept.

[tex] \\ [/tex]

Since we are given the value of the slope, we can substitute it into the equation:

[tex] \sf y = \dfrac{1}{2}x + b [/tex]

[tex] \\ [/tex]

We know that the line passes through (4 , 2), which means that the coordinates of this point verify the equation of the line. Therefore, we can substitute its coordinates into the equation and solve for b:

[tex] \sf (\overbrace{\sf 4}^{\sf x} \ , \ \underbrace{\sf 2}_{\sf y}) \\ \\ \sf \longrightarrow 2 = \dfrac{1}{2}(4) + b \\ \\ \longrightarrow \sf 2 = 2 + b \\ \\ \longrightarrow \sf 2 - 2 = 2 + b - 2 \\ \\ \boxed{\boxed{\sf b = 0}}[/tex]

[tex] \\ [/tex]

Therefore, the equation of the line is:

[tex] \boxed{\boxed{\sf y = \dfrac{1}{2}x }} [/tex]