Answer:
[tex]y=\frac{2}{3}x+\frac{4}{3}[/tex]
Step-by-step explanation:
Let's write the equation of the line in the slope-intercept form. That is, y= mx +c, where m is the slope and c is the y-intercept.
Identify 2 coordinates on the line to calculate the slope.
The 2 points are (1, 2) and (4, 4).
Slope
[tex]=\frac{y_1-y_2}{x_1-x_2}[/tex]
= [tex]\frac{4-2}{4-1}[/tex]
= [tex]\frac{2}{3}[/tex]
Substitute the value of the slope into m:
[tex]y=\frac{2}{3}x+c[/tex]
Substitute any point into the equation to find c:
When x= 1, y= 2,
[tex]2= \frac{2}{3}(1)+c[/tex]
Solve for c:
[tex]c= 2-\frac{2}{3}[/tex]
c= [tex]\frac{4}{3}[/tex]
Thus, the equation that represents the line is [tex]y=\frac{2}{3}x+\frac{4}{3}[/tex].
Additional:
Should you wish to learn more about slope-intercept form, do check out the following!
- https://brainly.com/question/26351470
