Straight-line graphs, parallel/perpendicular, length and area problems Key points • A straight line has the equation y = mx + c, where m is Practice questions 1 A2400 ch5g Version 1 1 September 2020 Answers 1 a y = 2x – 3 b y =
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A2400 ch5g | Version 1.1 | September 2020
Equation of a straight line
A LEVEL LINKS
Scheme of work: 2a. Straight-line graphs, parallel/perpendicular, length and area problemsKey points
• A straight line has the equation y = mx + c, where m is the gradient and c is the y-intercept (where x = 0). • The equation of a straight line can be written in the form ax + by + c = 0, where a, b and c are integers. • When given the coordinates (x 1 , y 1 ) and (x 2 , y 2 ) of two points on a line the gradient is calculated using the formulaExample 4 Find the equation of the line passing through the points with coordinates (2, 4) and (8, 7).
, , and c = 31 Substitute the coordinates into the
equation to work out the gradient of the line.2 Substitute the gradient into the
equation of a straight line y = mx + c.3 Substitute the coordinates of either
point into the equation.4 Simplify and solve the equation.
5 Substitute c = 3 into the equation
Practice questions
1 Write an equation for the line passing through each of the following pairs of points.
a (4, 5), (10, 17) b (0, 6), (-4, 8) c (-1, -7), (5, 23) d (3, 10), (4, 7) 2121
yy m xx 1 2x= 2 8x= 1 4y= 2 7y= 21
21
7431
8262
yy m xx 1 2 yxc=+ 1 42
2 c=´+ 1 3 2 yx=+ 21
21
yy m xx 1 2 yxc=+