Answer:
[tex]y = \frac{4}{3}x + 2[/tex]
Step-by-step explanation:
Find the equation for the line in slope-intercept form: [tex]y = mx + b[/tex]
where m is the slope (gradient) and b is the y-intercept.
To find the slope (m)
Choose 2 points on the line: (0, 2) and (6, 10)
Let (0, 2) = [tex](x_1,y_1)[/tex]
Let (6, 10) = [tex](x_2,y_2)[/tex]
Use the slope formula: [tex]m=\frac{y_2-y_1}{x_2-x_1} =\frac{10-2}{6-0} =\frac{4}{3}[/tex]
Therefore, [tex]y = \frac{4}{3}x + b[/tex]
To find the y-intercept
The y-intercept is when x = 0 (where the line intersects the x-axis).
By inspection, the line intersects the y-axis at y = 2.
Therefore, y-intercept = 2
So, [tex]y = \frac{4}{3}x + 2[/tex]
