Answer:
[tex]y=-\dfrac{5}{2}x+1[/tex]
Step-by-step explanation:
The given graph is a straight line that intersects the y-axis at (0, 1). It has a negative slope because the y-values decrease as the x-values increase.
The formula for a linear equation is:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Slope-intercept form of a linear equation}}\\\\\large\text{$y=mx+b$}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$m$ is the slope.}\\\phantom{ww}\bullet\;\;\textsf{$b$ is the $y$-intercept.}\\\end{array}}[/tex]
To find the slope, we can substitute two points on the line into the slope formula. Let's use points (2, -4) and (0, 1):
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-(-4)}{0-2}=-\dfrac{5}{2}[/tex]
Now, substitute the slope (m = -5/2) and the y-intercept (b = 1) into the slope-intercept formula:
[tex]y=-\dfrac{5}{2}x+1[/tex]
Therefore, the equation of the graphed line is:
[tex]\Large\boxed{\boxed{y=-\dfrac{5}{2}x+1}}[/tex]
