Answer:
[tex]y=\frac{-5}{4}x+5[/tex]
Step-by-step explanation:
Slope intercept form: [tex]y=mx+b[/tex] where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept (the value of y when the line crosses the y-axis)
1) Find the slope of the line ([tex]m[/tex])
To do this, we can plug the two given points (0,5) and (4,0) into the slope equation:
[tex]\frac{y_2-y_1}{x_2-x_1} \\= \frac{0-5}{4-0}\\= \frac{-5}{4}[/tex]
Therefore, the slope of the line is [tex]\frac{-5}{4}[/tex].
2) Find the y-intercept of the line ([tex]b[/tex])
Recall that the y-intercept is the value of y when the line crosses the y-axis. We don't actually need to perform any calculations because on the graph, we can see that the line crosses the y-axis when y=5.
Therefore, the y-intercept of the line is 5.
Plugging both [tex]m[/tex] and [tex]b[/tex] into [tex]y=mx+b[/tex], we have a final equation of:
[tex]y=\frac{-5}{4}x+5[/tex]
I hope this helps!
