Respuesta :
ANSWER
[tex]y=\frac{2}{3}x+\frac{4}{3}[/tex]EXPLANATION
We want to find the equation of the straight line given on the graph.
The general form of a linear equation is given as:
[tex]y=mx+b[/tex]where m = slope; b = y-intercept
To find the slope, we apply the formula for slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1, y1) and (x2, y2) are two points on the line
Let us pick (1,2) and (4,4)
Therefore, the slope is:
[tex]m=\frac{4-2}{4-1}=\frac{2}{3}[/tex]To find the equation, we now apply the point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]Therefore, we have that the equation of the line is:
[tex]\begin{gathered} y-2=\frac{2}{3}(x-1) \\ y-2=\frac{2}{3}x-\frac{2}{3} \\ y=\frac{2}{3}x-\frac{2}{3}+2 \\ y=\frac{2}{3}x+\frac{4}{3} \end{gathered}[/tex]That is the equation of the line.
