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.

Answered by Victoria I. Maths tutor

4019 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve the simultaneous equations (1) 2x+3y=3 and (2) 3x+2y=7


What is the highest common factor of 24 and 90?


Solve x^(2) + 7x + 6 = 0.


If the hypotenuse of a triangle is 7cm and another side is 4cm, what's the length of the other side? How can I work this out?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo
Cookie Preferences