Find the equation of the line that contains the given pair of points. (2,4) and (6,8) y=-x+2 y=(4)/(3)x+2 y=-x-2 y=x+2

To find the equation of the line that contains the given pair of points \((2,4)\) and \((6,8)\), we first need to determine the slope of the line. The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:<br /><br />\[<br />m = \frac{y_2 - y_1}{x_2 - x_1}<br />\]<br /><br />Substituting the given points \((2,4)\) and \((6,8)\):<br /><br />\[<br />m = \frac{8 - 4}{6 - 2} = \frac{4}{4} = 1<br />\]<br /><br />Now that we have the slope \(m = 1\), we can use the point-slope form of the equation of a line, which is:<br /><br />\[<br />y - y_1 = m(x - x_1)<br />\]<br /><br />Using the point \((2,4)\) and the slope \(m = 1\):<br /><br />\[<br />y - 4 = 1(x - 2)<br />\]<br /><br />Simplifying this equation:<br /><br />\[<br />y - 4 = x - 2<br />\]<br />\[<br />y = x + 2<br />\]<br /><br />Therefore, the equation of the line is \(y = x + 2\).<br /><br />The correct answer is:<br />\( y = x + 2 \)