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:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Thus, we have:
[tex]\begin{gathered} m=\frac{425-200}{4-1} \\ \\ m=\frac{225}{3} \\ \\ m=75 \end{gathered}[/tex]
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)
[tex]\begin{gathered} y=mx+b \\ \\ 200=75(1)+b \end{gathered}[/tex]
Let's solve for the y-intercept b.
[tex]\begin{gathered} 200=75+b \\ \text{Subtract 75 from both sides:} \\ 200-75=75-75+b \\ \\ 125=b \\ \\ b=125 \end{gathered}[/tex]
Therefore, the y-intercept is = 125.
The equation in slope-intercept form is:
[tex]y=75x+125[/tex]
ANSWER:
[tex]y=75x+125[/tex]
