PCH3: Linear Functions & Lines Flashcards
What is the gradient of a line parallel to the x-axis?
m=0
What is the gradient of a line parallel to the y-axis?
m is undefined
What is the gradient intercept form?
y = mx + b
where m= gradient
y intercept = b
Gradient formulas
m = tanø m = rise ÷ run
m = y2 - y1
———–
x2- x1
Equation of a straight line
y - y1 = m (x - x1)
General form
ax + by + c = 0
Equation of a straight line through two points
y - y1 = y - y2
——- ————-
x - x1 x - x2
Parallel lines
Have the same gradient
Perpendicular lines
m1m2 = -1
have reciprocal gradients
Calculating a POI
Can be found by using simultaneous equations and then checking by substituting POI into the original equations
Showing that a given line crosses through the POI
- Find POI
2. Sub values for POI into given equation
Finding equation of a line that crosses through a POI and another given point
- Sub equations into formula:
a1x + b1y + c1 + k(a2x + b2y + c2) = 0
- Sub given point values into formula to calculate k
- Sub value for k into the equation obtained from the first step
Key for regions determined by lines
- Unbroken line= line is included in region
- Broken line= line forms the boundary of but is not included in region
- To determine which side of the line the required region lies, sub coordinates of chosen point into inequality
Distance between two points formula
d = √ (x2 - x1)^2 + (y2-y1)^2
Perpendicular distance from a point to a line
d = | ax1 + by1 + c |
| —————— |
| √a^2 + b^2 |
