Question

Find the equation of the linear function represented by the table below in slope-intercept form

Answer 1

Answer:

$\huge\boxed{y=2x-2}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept → (0, b)

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

(x₁; y₁); (x₂; y₂) - points on a line

From the table we have

$(1,\ 0)\to x_1=1;\ y_1=0\\\\(2,\ 2)\to\ x_2=2;\ y_2=2$

Substitute:

$m=\dfrac{2-0}{2-1}=\dfrac{2}{1}=2$

Put the value of a slope and coordinates of the point (1, 0) to the equation of a line:

$0=2(1)+b$

$0=2+b$          subtract 2 from both sides

$-2=b\to b=-2$

Finally we have:

$y=2x-2$