Write the equation of a line that goes through the point (1,3) and the point (3,7) Hint: You need to find the slope first! y=3x-1 y=2x+1 y=x+2 y=3x-2

To find the equation of a line that goes through the points \( (1,3) \) and \( (3,7) \), 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 \( (1,3) \) and \( (3,7) \):<br /><br />\[<br />m = \frac{7 - 3}{3 - 1} = \frac{4}{2} = 2<br />\]<br /><br />Now that we have the slope \( m = 2 \), 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 \( (1,3) \) and the slope \( m = 2 \):<br /><br />\[<br />y - 3 = 2(x - 1)<br />\]<br /><br />Expanding this equation:<br /><br />\[<br />y - 3 = 2x - 2<br />\]<br /><br />Adding 3 to both sides to solve for \( y \):<br /><br />\[<br />y = 2x + 1<br />\]<br /><br />Therefore, the equation of the line is \( y = 2x + 1 \). The correct answer is:<br /><br />\( y = 2x + 1 \)