(especially if is a fraction)
If in doubt, SKETCH IT!Find the equation of the straight line with gradient 3 that passes through (5, 4).
We know that the gradient is 3 so the line takes the form
To find the value of c, substitute (5, 4) into the equation
Replace c with −11 to complete the equation of the line
y = 3x − 11
To find the value of c, substitute either of the given points into this equation. Here we will pick (8, 1) as it is doesn't contain negative numbers so is easier to work with
Replace c with −11 to complete the equation of the line
y = mx + c and ax + by = c
plot c on the y-axis
go 1 across, m up (and repeat until you can draw the line)put y = 0 to find x-axis intercept
(You may prefer to rearrange to y = mx + c and use above method)On the axes below, draw the graphs of and .
For , first plot c, which is (0, −1)
Then, as m = 3, . So plot a point 3 up and 1 right. Repeat at least once more and then join the points with a straight line. Extend the line to the edges of the grid.
The steps for are the same, but first we need to rearrange into the form y = mx + c
Now we can plot c, which is (0, 3)
For the gradient, . So plot a point 3 down and 5 right. There isn't space on the grid to repeat this so join the points with a straight line. Extend the line to the edges of the grid. The answer is shown above