2Q_Elective_A (Lesson1-5)

Linear Equation

is an equation whose solutions from a straight line on a coordinate plane and can be written in the form ax+by =c where a,b, and c are real numbers but a and b cannot be both zero.

Solutions

the solution of linear equation in two variables is an ordered pair that makes a true mathematical statement of the equation.

Slope/Gradient

the ratio of the change in vertical distance (rise) to the change in horizontal distance (run)

Straight Line 

it can be defined as one dimensional figure of zero width (thickness) that endlessly extends in both directions.

Slope/gradient

the direction towards which line is expanding can be determined by the line’s slope or gradient.

Positive Slope

the line will be increasing and it extends to the right moving upwards

Negative Slope

the line will be decreasing and it extends to the right moving downwards

Horizontal Line

if the slope is equal to 0, then the line is parallel to the x-axis

Vertical Line

if the slope is undefined, then the line is perpendicular to the x-axis.

Steepness of a Line

the higher the absolute value of the slope, the steeper the line is.

Perpendicular Lines

lines that meet each other such that 90 degrees is formed.

Intersecting Line 

lines that meet each other at some point

Parallel Line

lines that never meet each other. They are equidistant.

Equation of a line

a straight line on the coordinate plane can be described by the equation y= mx+b where m is the slope of the line and b is the intercept.

Equation of a Line given a slope and y-intercept

the equation of a line through the origin with a given gradient

x/a + y/b = 1

a line with a nonzero intercepts a and b has equation

X-intercept 

the point where the line passes through x-axis; the coordinates follow the form (x,0)

Y-intercept

the point where the line passes through y-axis; the coordinates follow the form (y,0)

Shortest Distance

the distance from a point to a line can be considered shortest distance from a given point on an infinite straight line 

Perpendicular Distance

the length of line segment joining the point to the nearest point on the line is the shortest distance from that point