Form 4 Chapter 5
Saturday, February 22, 2014 | 12:49 AM | 0 Rain[s]
Gradient of a Straight Line*Vertical distance and horizontal distance1. The diagram below show a straight line AB.
OA is known as the horizontal distance and OB is known as the vertical distance.
2.Vertical distance and horizontal distance are perpendicular to each other.
*Ratio of vertical distance to horizontal distance1.The gradient of a straight line is the ratio of the vertical distance to the horizontal distance between
two points on the straight line.
2.Vertical distance and horizontal distance are perpendicular to each other.
*Ratio of vertical distance to horizontal distance1.The gradient of a straight line is the ratio of the vertical distance to the horizontal distance between
two points on the straight line.
For example:
5.2 Gradient of a Straight Line in Cartesian Coordinates
*Formula for gradient of straight line The gradient,m,of a straight line passing through point P (x1,y1) and point Q (x1,y2)
*Formula for gradient of straight line The gradient,m,of a straight line passing through point P (x1,y1) and point Q (x1,y2)
5.3 Intercepts
*The x-intercept and the y-intercept of a straight line1.The x-intercept is the x-coordinate of the intersection point between a straight line and the x-axis.
2.The y-intercept is the y-coordinate of the intersection point between a straight line and the y-axis.
*The x-intercept and the y-intercept of a straight line1.The x-intercept is the x-coordinate of the intersection point between a straight line and the x-axis.
2.The y-intercept is the y-coordinate of the intersection point between a straight line and the y-axis.
*Intercepts and gradient of a straight lineGiven a straight line with x-intercept = a and y-intercept =b,
5.4 Equation of a Straight Line
*Drawing the graph given an equation y = mx + c 1.The graph of the linear equation u = mx + c is a straight line.To draw the graph,follow the steps below :
STEP 1 :Construct a table of values using any two values of x
STEP 2 :Plot the two points on a Cartesian plane
STEP 3 :Draw a straight line through these two points
*Determining whether a given points lies on a straight line1.If a point lies on a specific straight line y = mx + c,then the coordinates of the point satisfy the equation
of the straight line.
2.If a point does not lie on a specific straight line y = mx + c,then coordinates of the point does not
satisfy the equation of the line.
3.To determine whether a given points lies on specific straight line :STEP 1 :Substitute the value of x-coordinate and the value of y-coordinate into the equation
STEP 2 :Compare the values obtained on LHS AND RHS.
(a) If LHS = RHS, then the point lies on the straight line.
(b) If LHS ≠ RHS, then the point does not lie on the straight line.
*Writing the equation of a straight lineTo write the equation of a straight line,the values of m and c need to be identified.
5.4 Equation of a Straight Line
*Drawing the graph given an equation y = mx + c 1.The graph of the linear equation u = mx + c is a straight line.To draw the graph,follow the steps below :
STEP 1 :Construct a table of values using any two values of x
STEP 2 :Plot the two points on a Cartesian plane
STEP 3 :Draw a straight line through these two points
*Determining whether a given points lies on a straight line1.If a point lies on a specific straight line y = mx + c,then the coordinates of the point satisfy the equation
of the straight line.
2.If a point does not lie on a specific straight line y = mx + c,then coordinates of the point does not
satisfy the equation of the line.
3.To determine whether a given points lies on specific straight line :STEP 1 :Substitute the value of x-coordinate and the value of y-coordinate into the equation
STEP 2 :Compare the values obtained on LHS AND RHS.
(a) If LHS = RHS, then the point lies on the straight line.
(b) If LHS ≠ RHS, then the point does not lie on the straight line.
*Writing the equation of a straight lineTo write the equation of a straight line,the values of m and c need to be identified.
*Intercepts and gradient of a straight lineGiven a straight line with x-intercept = a and y-intercept =b,
5.4 Equation of a Straight Line
*Drawing the graph given an equation y = mx + c 1.The graph of the linear equation u = mx + c is a straight line.To draw the graph,follow the steps below :
STEP 1 :Construct a table of values using any two values of x
STEP 2 :Plot the two points on a Cartesian plane
STEP 3 :Draw a straight line through these two points
*Determining whether a given points lies on a straight line1.If a point lies on a specific straight line y = mx + c,then the coordinates of the point satisfy the equation
of the straight line.
2.If a point does not lie on a specific straight line y = mx + c,then coordinates of the point does not
satisfy the equation of the line.
3.To determine whether a given points lies on specific straight line :STEP 1 :Substitute the value of x-coordinate and the value of y-coordinate into the equation
STEP 2 :Compare the values obtained on LHS AND RHS.
(a) If LHS = RHS, then the point lies on the straight line.
(b) If LHS ≠ RHS, then the point does not lie on the straight line.
*Writing the equation of a straight lineTo write the equation of a straight line,the values of m and c need to be identified.
5.4 Equation of a Straight Line
*Drawing the graph given an equation y = mx + c 1.The graph of the linear equation u = mx + c is a straight line.To draw the graph,follow the steps below :
STEP 1 :Construct a table of values using any two values of x
STEP 2 :Plot the two points on a Cartesian plane
STEP 3 :Draw a straight line through these two points
*Determining whether a given points lies on a straight line1.If a point lies on a specific straight line y = mx + c,then the coordinates of the point satisfy the equation
of the straight line.
2.If a point does not lie on a specific straight line y = mx + c,then coordinates of the point does not
satisfy the equation of the line.
3.To determine whether a given points lies on specific straight line :STEP 1 :Substitute the value of x-coordinate and the value of y-coordinate into the equation
STEP 2 :Compare the values obtained on LHS AND RHS.
(a) If LHS = RHS, then the point lies on the straight line.
(b) If LHS ≠ RHS, then the point does not lie on the straight line.
*Writing the equation of a straight lineTo write the equation of a straight line,the values of m and c need to be identified.
*Determining the gradient and the y-intercept of a straight lineWhen the equation of a straight line is given in the from y = mx + c,then the gradient of the straight line is m and its y-intercept is c.
*Finding the equation of a straight lineI. The equation of a straight line that is parallel the x-axis or the y-axis
