The points A and B have coordinates (1, 2) and (5, 8) respectively. Find, in the form y = mx +c, an equation for the straight line through A and B.

Method 1:
Step 1: Note down the given points as well as assign these points with the variables
EXAMPLE: ( 7, 4 ) assign this point with (x_1, y_1)
( 2, 0 ) assign this point with (x_2,y_2)
................etc
Step 2: Calculate gradient or slope(m) from two points
FORMULA: \frac{y-change}{x-change},
or \frac{y_2 - y_1}{x_2 - x_1}
EXAMPLE: Slope of A(7, 4) and B(2, 0 )
\frac{4-0}{7-2} = \frac{4}{5}
Step 3: Substitute either values slope(m) and any one point into the equation of a straight line.
FORMULA: Equation of a straight line
y - y_1 = m(x - x_1)
Where m = slope and ( x_1, y_1) = any point
EXAMPLE: I took (2, 0) as a point and m = \frac{4}{5}
y - 0 = \frac{4}{5} ( x - 2)
5y = 4x - 8
Step 4: Simplify and make the equation in the form of Ax + By + C =0
Method 2:
Step 1: Note down the given points as well as assign these points with the variables
EXAMPLE: ( 7, 4 ) assign this point with (x_1, y_1)
( 2, 0 ) assign this point with (x_2, y_3)
................etc
Step 2: Substitute either given points in the formula.
FORMULA:
(y_1-y_2)x+\left(x_2-x_1)y+(x_1y_2-x_2y_1)\right)
Step 3: Simplify and make the equation in the form of Ax+ By + C =0