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Learn about the equation of a line in the Maths department at Millburn Academy. Understand horizontal, vertical, and sloping lines, and the general form of a linear equation.
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Millburn Academy Maths department Higher Equation of a Line y = mx + c
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.
Horizontal Lines What is the gradient of a horizontal line? 0 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..
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