1. Using the Point-Slope Form

Reviewing Equations of Lines

The point-slope form of an equation of a line is y  y1  mx  x1 , where x1 , y1  is any point on the line and “m” is the gradient or slope of the line.

The standard form of an equation of a line is Ax  By  C  0 . The A and B are numerical coefficients in front of the variables x and y and C is the constant term. The order is important. There is no fractions or decimals allowed in standard form. The leading coefficient in front of the x variable must be positive.

Eg1: Writing Equations Given a Point and the Slope

1 Write an equation in standard form for the line through A ( 3 , -4 ) with slope of  . 2

Eg2: Writing Equations Given Two Points

Write an equation in standard form for a line through A (-3, -2 ) and B (1 , 6 ).

2. Equations for Special Lines – Horizontal and Vertical Lines

All horizontal lines will have points with the same y co-ordinates. Therefore the equation for a horizontal line is ALWAYS y = _____. The slope of every horizontal line is . ** HOY **

All vertical lines will have points with the same x co-ordinates. Therefore the equation for a vertical line is ALWAYS x = ____. The slope of every vertical line is . ** VUX **

Eg3: Equations of Horizontal and Vertical Lines

Write an equation of; a) the horizontal line through C ( 2 , 3 ) b) the vertical line through D ( -4 , 1 )

of 3 Reviewing Equations of Lines

3. Using the Slope and y-intercept form

The equation y = mx + c is the slope and y-intercept form of a line. The gradient or slope is “m” and the y-intercept is “c”.

For a line defined by y  3x  5, the gradient or slope is and the y-intercept is .

Eg4: Finding the Slope and y-intercept Given an Equation

Find the slope and y-intercept of the line 2x  3y  6  0 .

4. Finding the x & y-Intercepts Given an Equation

Recall: An x-intercept is where the line crosses the x-axis. The ordered pair for all x-intercepts is (x , 0). Therefore, to find x-intercepts we let y = 0 and solve for the x-value. A y-intercept is where the line crosses the y-axis. The ordered pair for all y-intercepts is (0 , y). Therefore, to find a y-intercept we let x = 0 and solve for the y-value.

Eg5: Find the x & y-intercepts of 3x – 4y = -12

5. Sketch the following Lines

Eg6 a) y = -3/5 x + 2 b) 15x – 10y = 60 c) 7x + 3y – 14 = 0

of 3 Reviewing Equations of Lines

6. Parallel and Perpendicular Lines

The slopes of parallel lines are the same.

The slopes of perpendicular lines are negative reciprocals. The product of the slopes of perpendicular lines is -1.

3 Given the slope of a line is . 4 The slope of all lines which are parallel would be . The slopes of all lines which are perpendicular would be .

Eg7: Parallel Lines

Write an equation of the line that is parallel to 2x  y  5  0 and passing through the point A ( -1 , 5 ). State your final answer in standard form.

Eg8: Perpendicular Lines

Write an equation of the line perpendicular to 3x  y  6  0 and passing through the point P ( 5 , 2 ). State your final answer in standard form.