What is the equation of a line that has an x-intercept of -2 and a y-intercept of -5?

2 Answers
Jun 10, 2018

#y=-5/2x-5#

Explanation:

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

#•color(white)(x)y=mx+b#

#"where m is the slope and b the y-intercept"#

#"here "b=-5#

#y=mx-5larrcolor(blue)"is the partial equation"#

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

#•color(white)(x)m=(y_2-y_1)/(x_2-x_1)#

#"let "(x_1,y_1)=(-2,0)" and "(x_2,y_2)=(0,-5)#

#m=(-5-0)/(0-(-2))=(-5)/2=-5/2#

#y=-5/2x-5larrcolor(red)" is the equation of the line"#

Jun 10, 2018

#y=-5/2x - 4#

Explanation:

You have 2 points on the line:

#(-2,0), (0-5)#

Use slope point formula

First you determine the slope:

#(color(blue)(x_1),color(blue)(y_1)) = (-2,0)#

#(color(red)(x_2),color(red)(y_2))=(0,-5)#

#color(green)m =(color(red)(y_2)-color(blue)(y_1))/(color(red)(x_2)-color(blue)(x_1))#

#color(green)m =(color(red)(-5)-color(blue)(0))/(color(red)(0)-color(blue)((-2)))=-5/2#

Now use the Point Slope form of a line:

#(y-color(blue)(y_1)) = color(green)m(x-color(blue)(x_1))#

#(y-color(blue)((-5))) = color(green)(-5/2)(x-color(blue)(0))#

#y+5=-5/2x#

#y=-5/2x - 5#

graph{y=-5/2x - 5 [-10, 10, -5, 5]}