graphs

formula of a straight line

y=mx+c

where is the gradient and y-intercept in y=mx+c?

m = gradient

c = y-intercept

how do you find the gradient

change in y ÷ change in x

where would you find the y-intercept?

where the graph crosses the y-axis

if the line starts low and ends high, the gradient will be..

positive

if the line starts high and ends low, the gradient will be..

negative

how would you identify the gradient and y-intercept in y=mx+c?

\-rearrange to form y=mx+c (if needed)

\-read value of m (gradient) and c (y-intercept)

how would you find the gradient between two points?

\-find the change in x and change in y

\-substitute into change in y/change in x

how do you find the midpoint between two points?

\-add the x co-ordinates and halve them

\-add the y co-ordinates and halve them

to find an x-intercept, the y coordinate is always..

0

to find a y-intercept, the x coordinate is always..

0

how do you find a y-intercept?

\-substitute x=0

\-solve for y

how do you find a x-intercept?

\-substitute y=0

\-solve for x

how do you form an equation when given a point (x,y) or two points?

\-calculate gradient (if needed)

\-substitute your answer for m in the equation

\-substitute one pair of coordinates

\-find c

\-write the equation in the required form

what’s the formula for finding the distance between two points?

distance = √(x₂-x₁)²+(y₂-y₁)²

how do you find the distance between two points?

\-draw a diagram (optional)

\-find distances travelled in x and y direction ((x₂-x₁) and (y₂-y₁))

\-use pythagoras to find hypotenuse

parallel lines…

have the same gradient

perpendicular lines…

don’t have the same gradient

what is the product of two gradients of perpendicular lines?

\-1

how would you prove two lines are perpendicular?

the product of their gradients will be -1

or

the gradient will be the negative reciprocal of the other

how would you prove two lines are parallel/perpendicular?

\-rearrange all equations to y=mx+c form

\-if parallel, the gradient is the same/if perpendicular the product of the gradients is -1 or one gradient is the negative reciprocal of the other

how to find the equation of a line if it’s parallel/perpendicular to another given line?

\- find gradient of given line (if parallel, the gradient is the same/if perpendicular the product of the gradients is -1 or one gradient is the negative reciprocal of the other)

\-substitute given coordinates to find c

\-write complete equation

equation of a circle

x²+y²=r²

(when centre = (0,0) and radius = r)

where does tangent meet the radius?

at 90°

how to plot a linear graph using the cover up method:

(equation needs to be in the form ax+by=c)

\-cover the 𝑥 term, solve the resulting equation and plot this on the x-axis

\-cover the 𝑦 term, solve the resulting equation and plot this on the y-axis

\-draw a line through the two points plotted