It is required to find the equation of the given line in standard form.
Recall that the equation of a line in standard form is written as:
[tex]Ax+By=C[/tex]
Where A, B, C are constants.
The Equation of a line with a slope, m that passes through the point (x₁,y₁) in Point-Slope form is given as:
[tex]y-y_1=m(x-x_1)[/tex]
The slope formula for a line that passes through points (x₁,y₁) and (x₂,y₂) is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Notice from the graph that the line passes through points (2,0) and (4,5).
Substitute (x₁,y₁)=(2,0) and (x₂,y₂)=(4,5) into the slope formula to find the slope:
[tex]m=\frac{5-0}{4-2}=\frac{5}{2}[/tex]
Substitute m=5/2 and the points (x₁,y₁)=(2,0) into the point-slope form of the equation of a line:
[tex]\begin{gathered} y-0=\frac{5}{2}(x-2) \\ \Rightarrow y=\frac{5}{2}x-\frac{5}{2}(2) \\ \Rightarrow y=\frac{5}{2}x-5 \end{gathered}[/tex]
Next, rewrite the equation in the standard form of the equation of a line:
[tex]\begin{gathered} y=\frac{5}{2}x-5 \\ \Rightarrow y-\frac{5}{2}x=-5 \\ \Rightarrow-\frac{5}{2}x+y=-5 \end{gathered}[/tex]
The required equation in standard form is -5/2 x+ y = -5.
