Let’s review some of the things we’ve learnt about linear graphs this week.
Something that some of you found difficult was finding the coordinates of the points where a straight line crosses the axes. Remember, everywhere on the x-axis, y = 0. So to find the coordinates of where a line crosses the x-axis then substitute y = 0 into the equation of the line to find a value for x. The same method works for the y-axis (substitute x = 0). Here’s an example.
Where does the line 5x + 3y = 15 cross the axes?
It crosses the x-axis where y = 0. Substitute y = 0 into the equation to get 5x = 15, so x = 3. So the point is (3,0).
It crosses the y-axis where x = 0. Substitute x = 0 into the equation to get 3y = 15, so y = 5. So the point is (0,5).
We also learnt how to find the length of a line segment (draw a sketch and use Pythagoras) and how to find the midpoint of a line (add the two x coordinates and two y coordinates together and divide by two). Here’s the four questions we did in class, with answers.
Another thing we discussed was how to tell whether a point is on a line. If asked whether the point (4,7) lies on the line y = 2x + 1 then you can substitute x = 4 and see if you get y = 7 (in this case you don’t, so the point is not on the line).
We learnt that if two lines are parallel they have the same gradient. If two lines are perpendicular then the gradient of one line is the negative reciprocal of the gradient of the other line. For more practice of parallel and perpendicular lines try the questions on this website. Here’s the worksheet we did in class.
