Question

Please help with the image below.(?)

Answer 1

I tried this:

Explanation:

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

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`

Answer 2

`"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"`