Question

What Is the equation of the graph? y=7/4x-5/2y=3/2x-5/2y=5/2x+3/2y=-5/2x+3/2​

Answer 1

Answer:

A

Step-by-step 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 = $\frac{1+2.5}{2-0}$ = $\frac{3.5}{2}$ = $\frac{7}{4}$

Note the line crosses the y- axis at (0, - 2.5) ⇒ c = - 2.5 = - $\frac{5}{2}$

y =  $\frac{7}{4}$ x - $\frac{5}{2}$ → A

Answer 2

Answer:  $y=\dfrac{7}{4}x-\dfrac{5}{2}$

Step-by-step explanation:

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

$(y-b)=\dfrac{d-b}{c-a}(x-a)$

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:-

$(y-1)=\dfrac{1-(-2.5)}{2-0}(x-2)\\\\\Rightarrow\ (y-1)=\dfrac{1+2.5}{2}(x-2)\\\\\Rightarrow\ y-1=\dfrac{3.5}{2}(x-2)\\\\\Rightarrow\ y-1=\dfrac{7}{4}(x-2) \ \ [\because 3.5=\dfrac{7}{2}]\\\\\Rightarrow\ y-1=\dfrac{7}{4}x-\dfrac{7}{4}\times2\\\\\Rightarrow\ y=\dfrac{7}{4}x-\dfrac{7}{2}+1\\\\\Rightarrow\ y=\dfrac{7}{4}x+\dfrac{-7+2}{2}\\\\\Rightarrow\ y=\dfrac{7}{4}x-\dfrac{5}{2}$

Hence, the equation of the graph is $y=\dfrac{7}{4}x-\dfrac{5}{2}$