Question

Find the equation of the line shown.

Answer 1

Equation is y = -2x + 9

Explanation:

At point (x, y) the linear equation of a line with gradient m is given as;

`{ \pmb{y = mx + c}} \\`

Consider two points; (4, 1) and (3, 3) from the graph above;

For gradient;

`{ \tt{m = ((3 - 1))/(3 - 4) }} ={ \tt{ (2)/( - 1) }} \\ \\ { \tt{m = - 2}}`

Therefore;

`{ \tt{y = - 2x + c}}`

Consider point (4, 1);

`{ \tt{1 = ( - 2 * 4) + c}} \\ { \tt{c = 9}}`

Therefore,

`{ \boxed{ \tt{ \: y = - 2x + 9 \: }}}`