Equation of a Straight Line

Midpoint formula

(X1+X2/2, Y1+Y2/2)

Straight lines with positive gradient

/

y = y₁

parallel to x-axis

x = x₁

parallel to y-axis

y - y₁ = m(x - x₁)

point-slope

y = mx + b

slope-intercept

If the line is dotted

the sign remains as the more than/less than sign

y - y₁/x - x₁ = y₂ - y₁/x₂-x₁

two-point

If the region is below

use the less than sign

If the region is above

use the more than sign

If the line is straight

use the more than/less than or equal to sign

90 = 60x

x = 1.5

180 = 12x

x = 15

10 + 10x = 180

x = 17

10x = 180

x = 18

10 + 4x = 90

x = 20

6x = 180

x = 30

5x = 180

x = 36

10 + 2x = 90

x = 40

2x =90

x = 45

3x = 180

x = 60

10x = 90

x = 9

2x = 180

x = 90

X

= How far along

Y or Intercept

= How far up

M or Slope

= How steep the line is

Y

= Intercept

M

= Slope

B

= Where the line crosses the Y axis

gradient

A difference in concentration, pressure, or electrical charge between two regions.

perpendicular

At an angle of 90˚ to a given line, plane, or surface.

linear equation

Equation for a straight line

y-y1= m (x-x1)

Equation of a line (if you know the gradient and one coordiante)

Y-Y1/Y2-Y1 = X-X1/X2-X1

Equation of a line (if you know two coordinates on a line)

y2-y1/x2-x1

Gradient of a line

m1= -1/m2

Gradient of a perpendicular line

(x1+x2/2), (y1+y2/2)

Midpoint

parallel

Phrases or sentences of a similar construction/meaning placed side by side, balancing each other

m1 x m2= -1

Proof two lines are perpendicular

Determine which point on the graph the line passes through. Is it the x or y axis?

Step 1

Using this number form an equation in the form x = ? or y = ?

Step 2

Determine if the region you are describing is below or above this number

Step 3

Determine if the line is straight or dotted

Step 4

Gradient

Tells you how steep the line is

y-intercept

The Y-coordinate of the point where the line crosses the y-axis. (Y,0)

distance between two points

The absolute value of the difference of the coordinates of the points.

x-intercept

The coordinate at which a graph intersects the x-axis. The X-coordinate of the point where a line crosses the x-axis (X.0)

What is x

The gradient

Length of a line formula

The square root of (X1-X2)squared + (Y1-Y2) squared

What is c

The y intercept

What is the rule for the gradient of two perpendicular lines?

Their gradients multiply to -1

What is the rule for parallel lines?

They have the same gradient

To Find Slope

Use the Rise over Run

Y-intercept

Where the line cuts the axis

Gradient formula

Y1-Y2/X1-X2

The equation of a straight line

Y=mx+c

Vertical line

You only know X axis

Straight lines with negative gradient

\

mid-point

a point equidistant from the ends of a line or the extremities of a figure

x/a + y/b = 1

intercept

Gradient formula

m= y2-y1 / x2-x1

Equation

y= mx+c

slope intercept form

y=mx+b