Millburn Academy Maths department Higher Equation of a Line y = mx + c

where m is the gradient and c is the y-intercept. In National 5 you learned that the equation of a straight line is given by the formula: y = mx + c where m is the gradient and c is the y-intercept. O eg the line y = 2x - 1 crosses the y axis at (0,-1) and has a gradient of 2.

What is the gradient of a horizontal line? Horizontal Lines What is the gradient of a horizontal line? Since this horizontal line has a gradient of 0 and it crosses the y axis at the point (0,2) its equation is: O y = 0x + 2 simplified y = 2 All horizontal lines have an equation of the form y = k where k is the y-intercept. ie all point on a horizontal line have the same y coordinate.

∞ Vertical Lines What is the gradient of a vertical line? All points on a vertical line have the same x-coordinate. In this example all points have an x-coordinate of 3. O Therefore the equation of this line is x = 3 All vertical lines have an equation of the form x = k where k is the point of intersection with the x-axis..

Horizontal lines have equation: y = k Summary Horizontal lines have equation: y = k where k is the point of intersection with the y-axis. O Vertical lines have equation: x = k Sloping lines have equation: y = mx + c where k is the point of intersection with the x-axis. where m is the gradient and c is the y intercept

General Form of the Linear Equation The equation of the line is:   We can rearrange this into the form: ax + by + c = 0 This is the general form of a linear equation. O