How can I find the equation of a line l which passes through the points (5,7) and (3, -1)

First thing first, we should always write down the equation of a straight line (which is y = mx + c) as this will be important for this question.In order to find the equation of the straight line l we need to work out the gradient of the line between the two points and the y intercept of the line.Finding the gradient of the line (m):The formula we need to use to find the gradient is m = (difference in y values)/(difference in x values).In this example, the difference in y values = 7 - - 1 = 8 and the difference in x values = 5 - 3 = 2.Therefore the gradient m = 8/2 = 4.Finding the y-intercept:Since we have found the gradient of the line, our equation of our line l currently looks like y = 4x + c.To find c, we can substitute one of our points into our equation for l. If we substitute the point (3, -1) into our equation we get: -1 = 4(3) + c so c = -13.Therefore, the equation of the line l must be y = 4x - 13