<p> Reviewing Equations of Lines</p><p>1. Using the Point-Slope Form</p><p>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.</p><p>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.</p><p>Eg1: Writing Equations Given a Point and the Slope</p><p>1 Write an equation in standard form for the line through A ( 3 , -4 ) with slope of  . 2</p><p>Eg2: Writing Equations Given Two Points</p><p>Write an equation in standard form for a line through A (-3, -2 ) and B (1 , 6 ).</p><p>2. Equations for Special Lines – Horizontal and Vertical Lines</p><p>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 **</p><p>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 **</p><p>Eg3: Equations of Horizontal and Vertical Lines</p><p>Write an equation of; a) the horizontal line through C ( 2 , 3 ) b) the vertical line through D ( -4 , 1 )</p><p>Page 1 of 3 Reviewing Equations of Lines</p><p>3. Using the Slope and y-intercept form</p><p>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”.</p><p>For a line defined by y  3x  5, the gradient or slope is and the y-intercept is .</p><p>Eg4: Finding the Slope and y-intercept Given an Equation</p><p>Find the slope and y-intercept of the line 2x  3y  6  0 .</p><p>4. Finding the x & y-Intercepts Given an Equation</p><p>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.</p><p>Eg5: Find the x & y-intercepts of 3x – 4y = -12</p><p>5. Sketch the following Lines</p><p>Eg6 a) y = -3/5 x + 2 b) 15x – 10y = 60 c) 7x + 3y – 14 = 0</p><p>Page 2 of 3 Reviewing Equations of Lines</p><p>6. Parallel and Perpendicular Lines</p><p>The slopes of parallel lines are the same.</p><p>The slopes of perpendicular lines are negative reciprocals. The product of the slopes of perpendicular lines is -1.</p><p>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 .</p><p>Eg7: Parallel Lines</p><p>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.</p><p>Eg8: Perpendicular Lines</p><p>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.</p><p>Page 3 of 3</p>