Question

Slope=
Y- intercept=
Equation=

Answer 1

⇒To get the slope it requires us to have two points
`(x_(1) ,y_(1) ) \\(x_(2) ,y_(2) )`

⇒you can take any two points of your choice

I will take (1,5) and (2,10)

⇒To calculate the slope of the line we use the formula

`m=(y_(2) -y_(1) )/(x_(2) -x_(1) )`

where m is the variable that represent the slope of the line.

Let us substitute the points and simplify to get the slope.

⇒
`m=(10-5)/(2-1) \\m=(5)/(1) \\m=5`

⇒The gradient of the line is equal to 5

⇒ the general equation of finding the equation of a straight line is y=mx+c

where y is the y coordinate,

x is the x coordinate

and c is the y-intercept that you want in this case.

⇒To get it in the place of x and y in the general equation choose any point of your choice and plug it in.

⇒You already have the known variable m which is the slope in this case equal to 5.

⇒You can plug in any point of your choice in the picture as you would still get the same value of the y-intercept represented by letter c in the equation.

⇒I will use the point (2,10) in the place of (x,y)

`y=mx+c\\10=5(2)+c\\10=10+c\\c=10-10\\c=0`

⇒As indicated in the calculation the y intercept is 0 as c=0

⇒Now for the equation according to the values we find previously m=5

c=0

∴ the equation of this straight line is y=5x+0

simply because 0 has no effect ∴ y=5x