Question

Question #c018f

Answer 1

y = 5x + 17

Explanation:

The first step here is to calculate the gradient of the line passing through the 2 given points using the `color(blue)" gradient formula "`

`color(red)(|bar(ul(color(white)(a/a)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(a/a)|)))`
where `(x_1,y_1)" and " (x_2,y_2)" are 2 points"`

let `(x_1,y_1)=(2,3)" and " (x_2,y_2)=(1,-2)`

`rArr m=(-2-3)/(1-2)=(-5)/(-1)=5`

The equation of a line is `color(blue)" y=mx+c"`
where m represents the gradient and c, the y-intercept.

Since the lines are parallel , then m = 5, parallel lines have equal gradients.

Partial equation is y = 5x + c, and to find c , substitute (-3 ,2) into the partial equation.

x = -3 , y =2 : `5xx(-3)+c=2 rArr c=17`

and the full equation is y = 5x + 17