1. y=mx+c
1.1. y=Mx+c in which the m is the gradient.
1.1.1. If the gradient is a positive number then the line will be going in an upwards direction as in an upwards slope
1.1.2. If the gradient is a negative number then the line will be going in a downwards direction as in a downwards slope
1.2. y=mX+c in which the x literally stands for 1
1.2.1. For example if the equation is y=x+c that would mean the gradient is 1
1.2.2. For example if the equation is y=23x+2 then the gradient would be 23
1.3. y=mx+C in which the c stands for the y intercept
1.3.1. For example if the equation is y=mx+5 then the line would cross the y-axis at the 5.
1.4. (Cautionary note) it may show that y=mx without the c as the c or the y-intercept is at 0 and therefore makes no difference to the equation
1.4.1. (Also look at desmos, a website, for better understanding of how the line graphs work and the difference it make to alter one of the components slightly
2. y=3x+1232131 is parallel to y=3x+1
2.1. THis because the gradient is the same so therfore the two lines wil never touch each other despite the "c" being different.
3. Axis
3.1. The equations of axis
3.1.1. The equation for the x axis is y=0
3.1.2. The equation for the y axis is x=0
4. Question tips.
4.1. A line passes through the point (0,5) and has a slope of -3. Write its equation.
4.1.1. Answer: y=-3+5 as -3 is the slope (gradient) and it passes THOUGH A POINT (y interception) at (0,5) so it is plus 5
4.2. If y=mx+c passes through points (1,2) and (3,6) what are the values of m and c?
4.2.1. Slope equals (6-2) divided by (3-1) to find the difference and how much it changed by which equals 4 divided by 2 which equals 2 so as of now it is y=2x+???
4.2.1.1. To find out c we have to do y=2x+c and then 2+2 times 1 (since m equals two and x equals 1) which means the slope times the x value and is 2=2 so the c is 0.
4.2.1.1.1. The answer is y=2x (remember that if the y intercept(c) is 0 it does not need to be included.