#### The points A and B have coordinates (4, 6) and (12, 2) respectively. The straight line l_1 passes through A and B.

(a) Find an equation for l_1 in the form ax + by = c, where a, b and c are integers.

Anonymous

0

(a) Find an equation for l_1 in the form ax + by = c, where a, b and c are integers.

Krishna

0

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