Show that the lines y=3x+7 and 2y-6x=8 are parallel (not using a graphical method).
The standard form of a straight line is y = mx + c, where y and x are variables that depend on each other, m is the gradient and c is the y-axis intercept. An important fact for this question is that parallel lines have the same gradient.We see the first line is already in the standard form of a line and we can see from inspection that the gradient of y = 3x + 7 is 3.We now seek to get the second line in the same form. By adding 6x to both sides we see that 2y = 6x + 8.Now simply dividing by 2 on both sides we get y = 3x + 4 and we can see that the gradient of this line is also 3Hence the lines are parallel.
MB
Related Maths GCSE answers
All answers ▸Solve the following simultaneous equations: 2x-3y=16 x+2y=-6
Draw the graph of y=2-3x for values of x from -3 to 3.
When do I use a cosine rule over a sine rule?
Consider an isosceles triangle ABC, where AB=AC=1, M is the midpoint of BC, and <BAM=<CAM=x. Use trigonometry to find an expression for BM and by finding BC^2, show that cos2x = 1 - 2(sinx)^2.