Question

What Is the equation of the graph?

y=7/4x-5/2
y=3/2x-5/2
y=5/2x+3/2
y=-5/2x+3/2​

Answer 1

A

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, - 2.5) and (x₂, y₂ ) = (2, 1) ← 2 points on the line

m =
`(1+2.5)/(2-0)` =
`(3.5)/(2)` =
`(7)/(4)`

Note the line crosses the y- axis at (0, - 2.5) ⇒ c = - 2.5 = -
`(5)/(2)`

y =
`(7)/(4)` x -
`(5)/(2)` → A

Answer 2

Answer:
`y=(7)/(4)x-(5)/(2)`

Explanation:

The equation of a line passing through points (a,b) and (c,d) is given by :-

`(y-b)=(d-b)/(c-a)(x-a)`

From the given graph , it can be seen that the line is passing through (0,-2.5) and (2,1).

Then, the equation of line passing through (0,-2.5) and (2,1) will be:-

`(y-1)=(1-(-2.5))/(2-0)(x-2)\\\\\Rightarrow\ (y-1)=(1+2.5)/(2)(x-2)\\\\\Rightarrow\ y-1=(3.5)/(2)(x-2)\\\\\Rightarrow\ y-1=(7)/(4)(x-2) \ \ [\because 3.5=(7)/(2)]\\\\\Rightarrow\ y-1=(7)/(4)x-(7)/(4)*2\\\\\Rightarrow\ y=(7)/(4)x-(7)/(2)+1\\\\\Rightarrow\ y=(7)/(4)x+(-7+2)/(2)\\\\\Rightarrow\ y=(7)/(4)x-(5)/(2)`

Hence, the equation of the graph is
`y=(7)/(4)x-(5)/(2)`