Question

Write a linear equation in slope-intercept form for the graph shown

Answer 1

Given the points:

(x1, y1) ==> (1, 200)

(x2, y2) ==> (4, 425)

Let's write a linear equation in slope-intercept form for the gfraph shown using the two points.

Apply the slope intercept form:

y = mx + b

Where m is the slope and b is the y-intercept.

To find the slope, apply the formula:

`m=(y2-y1)/(x2-x1)`

Thus, we have:

`\begin{gathered} m=(425-200)/(4-1) \\ \\ m=(225)/(3) \\ \\ m=75 \end{gathered}`

The slope of the line is 75 .

Substitute 75 for m, then input the values of one point for the values of x and y.

Take the first point: (1, 200)

`\begin{gathered} y=mx+b \\ \\ 200=75(1)+b \end{gathered}`

Let's solve for the y-intercept b.

`\begin{gathered} 200=75+b \\ \text{Subtract 75 from both sides:} \\ 200-75=75-75+b \\ \\ 125=b \\ \\ b=125 \end{gathered}`

Therefore, the y-intercept is = 125.

The equation in slope-intercept form is:

`y=75x+125`

ANSWER:

`y=75x+125`