Find the equation of the line L passing through (0, 3) and (5, 7). What would the gradient of a line perpendicular to this line be? What about a line parallel to it?

Since L is a straight line between two points, it has the form y=mx+c, where m is the gradient. To find m we use that it is the difference in y values of the points divided by the difference in x values, ie (7-3)/(5-0) = 4/5. So now we have y = 4/5 x +c. To find c, substitute (0, 3) into this equation and solve it: 3 = 4/5 . 0 +c so c = 3. So the equation of the line is y = 4/5 x + 3.The gradient of a line perpendicular to L is the negative reciprocal of 4/5, so it is -5/4 (just swap the numerator and denominator and put a minus sign in front).The gradient of a line parallel to L is the same as the gradient of L : 4/5.