Question

Given the graph above find an equation for the graph and write your anwser in slope intercept form

Answer 1

Given:

Given that the graph of a linear function.

We need to determine the equation of the graph in slope intercept form.

Slope:

Consider any two coordinates from the equation of the line to determine the slope.

Let the two coordinates are (-4,3) and (4,-1)

The slope can be determined using the formula,

`m=(y_2-y_1)/(x_2-x_1)`

Substituting the coordinates in the above formula, we get;

`m=(-1-3)/(4+4)`

`m=(-4)/(8)`

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

Thus, the slope of the equation is
`m=-(1)/(2)`

Value of y - intercept:

The value of y - intercept is the value of y when x = 0.

Hence, from the graph, it is obvious that the value of y when x = 0 is 1.

Hence, the value of y - intercept is 1.

Thus, y - intercept is
`b=1`

Equation of the line:

The equation of the line can be determined using the formula,

`y=mx+b`

Substituting the slope
`m=-(1)/(2)` and the y - intercept
`b=1`

Thus, we get;

`y=-(1)/(2)x+1`

Thus, the equation of the line is
`y=-(1)/(2)x+1`