Question

In the X Y -plane, a line crosses the Y - axis at the point (0,3) and passes through the point ( 4,5). Which of the following is an equation of the line?A. y = x + 3 2B. y = 2x + 31 C. y = x – 4 2D. y = 2x – 4

Answer 1

Given two points of a line (x1, y1) and (x2, y2), the equation of the line is:

$\begin{equation*} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \end{equation*}$

We are given the points (0, 3) and (4, 5). Plugging in these values:

$y-3=\frac{5-3}{4-0}(x-0)$

Operating and simplifying:

$\begin{gathered} y-3=\frac{2}{4}x \\ \\ y=\frac{1}{2}x+3 \end{gathered}$