Here's a graph of a linear function. Write the equation that describes that function

We will write equation of our given function in slope-intercept form of line [tex]y=mx+b[/tex], where, m represents slope of the line and b represents y-intercept or initial value of the function.

We can see from our graph that at x equals 0 y is -3, so our y-intercept or initial value of our function will be -3.

Now let us find slope of our function using slope formula.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], where,

[tex]y_2-y_1[/tex]= Difference between two y-coordinates.

[tex]x_2-x_1[/tex]= Difference between same x-coordinates of two y-coordinates.

Upon substituting coordinates of points (0,-3) and (6,0) in slope formula we will get,

[tex]m=\frac{0--3}{6-0}[/tex]

[tex]m=\frac{0+3}{6}[/tex]

[tex]m=\frac{3}{6}[/tex]

[tex]m=\frac{1}{2}[/tex]

Let us substitute [tex]m=\frac{1}{2}[/tex] and b=-3 in slope-intercept form of equation.

[tex]y=\frac{1}{2}x-3[/tex]

[tex]y=0.5x-3[/tex]

Therefore, the equation [tex]y=0.5x-3[/tex] represents our given function.

zainebamir540 zainebamir540 · Answer 2 · 2019-03-03T19:00:10+01:00

Answer:

y = 0.5x-3

Step-by-step explanation:

We have given a graph of linear function.

We have to find the equation that describes that function.

y = mx+c is equation of line where m is slope and c is y-intercept.

Slope = m = y₂-y₁/x₂-x₁

From graph , we observed that

(0,-3) and (6,0) are points on graph.

Putting above values in slope formula, we have

Slope = m = 0-(-3)/6-0

Slope = m = 3 / 6

slope = m = 1/2 = 0.5

y-intercept is (0,-3).

Hence,

y = (.5)x+(-3)

y = 0.5x-3 is equation of graph that describes the linear function.