# Question #c018f

##### 1 Answer

May 1, 2016

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