Answer:
[tex]\mathsf{y=-\dfrac13x+5}[/tex]
Step-by-step explanation:
Slope-intercept form of a linear equation: [tex]\mathsf{y=mx+b}[/tex]
(where m is the slope and b is the y-intercept)
From inspection of the graph, the y-intercept is at (0, 5)
Therefore, b = 5
Choose another point on the line, e.g. (3, 4)
Now use the slope formula to find the slope:
[tex]\mathsf{slope=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
where:
- [tex]\mathsf{(x_1,y_1)=(0,5)}[/tex]
- [tex]\mathsf{(x_2,y_2)=(3,4)}[/tex]
[tex]\implies \mathsf{slope=\dfrac{5-4}{0-3}=-\dfrac13}[/tex]
Therefore, the equation of the line is:
[tex]\mathsf{y=-\dfrac13x+5}[/tex]
