How do you write a linear function equation that passes through points (-2,5) and (-4,7)?

1 Answer
Nov 26, 2016

#y=-x+3#

Explanation:

The equation of a line in #color(blue)"point-slope form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))#
where m represents the slope and # (x_1,y_1)" a point on the line"#

To calculate m, use the #color(blue)"gradient formula"#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))#
where # (x_1,y_1),(x_2,y_2)" are 2 points on the line"#

The 2 points here are (-2 ,5) and (-4 ,7)

#rArrm=(7-5)/(-4-(-2))=2/(-2)=-1#

Use either of the 2 given points for # (x_1,y_1)#

substitute m = - 1 and (-2 ,5) into the equation.

#y-5=-1(x+2)rArry-5=-x-2#

which simplifies to.

#y=-x+3#