How can I work out the equation of a line defined by 2 known points?

We know that the equation of a line takes up the slope-intercept form: y = mx + n,where m is the slope and n is the y intercept To work out the equation of the line for our 2 points, we use the point-slope formula: y - y1 = m(x - x1)where m is the slope and x1 and y1 are the coordinates of a point on the line.In our case, we know that A (5, 2) is a point on the line so x1 = 5 and y1 = 2.In order to use the point-slope formula, we also need to work out the slope of the line. We know that the slope has the formula: m = change in y/change in x = yB - yA/ xB - xA,where xA and yA represent the coordinates of point A, in our case, xA = 5 and yA = 2.and, similarly, xB and yB represent the coordinates of point A, in our case, xB = 1 and yB = 6.We substitute the values that we know in the formula above to work out the slope.=> m = 6 - 2/ 1 - 5=> m = 4/-4=> m = -1 We work out the equation of the line by using m, x1 and y1 in the point-slope formula: y - y1 = m(x - x1)y - 2 = -1(x - 5)We simplify this equation, putting it in the form: y = mx + n=> y - 2 = -x + 5=> y = -x + 7 The equation of the line is: y = -x + 7.

DF
Answered by Daria F. Maths tutor

4908 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Two apples and three bananas cost a total of £1.30. Seven apples and one banana cost a total of £1.70. Find the cost of a) one apple and b) one banana.


There are 300 students at a school who have been asked to attend assembly. 1/10 students are sat on chairs, 85% of students are sat on the floor, the rest do not attend assembly. How many students did not attend assembly?


A ball, dropped vertically, falls d metres in t seconds. d is directly proportional to the square of t. The ball drops 45 metres in the first 3 seconds. How many metres does the ball drop in the next 7 seconds?


Paul travels from Rye to Eston at an average speed of 90 km/h. He travels for T hours. Mary makes the same journey at an average speed of 70 km/h. She travels for 1 hour longer than Paul. Work out the value of T


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning