(Q14) To find the equation when given the gradient and one set of points (or coordinates), you have to solve for b.
1. Identify the gradient and x- and y- intercepts.
m=3, x=1, y=5
2. Substitute them into the equation, y=mx+b.
5=3(1) + b
3. Solve for b.
5=3 + b
b=2
4. Rewrite the equation.
y=3x+ 2
(Q15) To find the equation when given two sets of points, you need to.
1. Find the gradient, using the formula, (x2-x1 / y2-y1)
(7,5) and (4, -7)
x1=7, x2= 4, y1=5, y2=-7
4-7/-7-5 = -3/-12 = 1/4
Therefore, gradient = 1/4
2. Substitute with one set of points (can be either (7,5) or (4,-7) in this example - question 15) into the equation, (like you did in question 14)
a) Identify the gradient and x- and y- intercepts.
m=1/4, x=7, y=5
b) Solve for b.
5=1/4(7) + b
5=7/4 + b
b=13/4 or 3 1/4
c) Rewrite the equation.
y=1/4x + 13/4