Please help with the image below.(?)

enter image source here

2 Answers
Gió
Aug 8, 2018

I tried this:

Explanation:

You can see the #y-#intercept observing that your line passes through #y=-5#.

enter image source here

So the intercept will be the point #P1# of coordinates #x=0,y=-5#.

The slope #m# will be given as:

#m=(Deltay)/(Deltax)=(y_2-y_1)/(x_2-x_1)=(0-(-5))/(2-0)=5/2#

where we used two points #P2 and P1# on the graph and their coordinates.

The equation of the line can be found remebering its general form (using for example the coordinates of point #P2#):

#y-y_2=m(x-x_2)#

giving:

#y-0=5/2(x-2)#

#y=5/2x-5#

Jim G.
Aug 8, 2018

#"see explanation"#

Explanation:

#"the gradient is a measure of ""change in y"/"change in x"=(Deltay)/(Deltax)#

#"we require to have 2 points on the line "#

#(2,0)" and "(0,-5)" are 2 points on the line"#

#"note that "y=-5color(red)" is the y-intercept"#

#"gradient (m) "=5/2#

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

#•color(white)(x)y=mx+c#

#"where m is the gradient and c the y-intercept"#

#"here "m=5/2" and "c=-5#

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

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