Linear graphs and simultaneous linear equations

Equation of straight lines

• y= mx+ c —> m= gradient of the line, c= y intercept

• gradient of line= y2-y1/ x2-x1 —> find the coordinates by forming a right angled triangle on the line and taking the two coordinates at the start and the end on the triangle.

• m and c are constants

• horizontal= —

• vertical= |

• gradient of horizontal line—> y=c —> because a horizontal line does not have a gradient so m, is taken out of the equation.

• equation of vertical line—> x=a —> a is the x-intercept on the line.

• gradient of vertical line= undefined.

Graphs of Liner Equations in the form of ax+by=k

Solving Simultaneous Linear Equations using Elimination method

• Label each of the equations 1 and 2 respectively.

• the formula goes, 1-2

• if there are no same variable (in the situation you cannot eliminate anything) you should times the or both equations to get the lowest common multiple between them.

• the new multiplied equations are called 3 and 4/ or just 3 if only one equation had to be multiplied.

• if you had multiplied the/ a equation, the next step would be —> 1/2 -/+ 3/4 —> whether or not you subtract or add depends on the question and the variable. if the variable is a positive and negative than we would add. but if it was a negative and negative, then we would subtract.

• after getting the answer to either x or y, you should substitute it with an equation, either 1 or 2 and find out what x/y is (depending on which you found first)

• after finding out x/y, you check your answer by substituting both x and y in equation 1/2 (depending on which you didn't use before) and checking if the answer is the same as given in the question.