slope = -5/4
The y value of y intercept is 5
[tex]\begin{gathered} E\text{quaton of the line:} \\ y\text{ = }\frac{-5}{4}x\text{ + 5} \end{gathered}[/tex]
Explanation
To get the slope of the line, we will pick any two points on the line
using points: (0, 5) and (8, -5)
We will apply the slope formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} x_1=0,y_1=5,x_2=8,y_2\text{ = }-5 \\ In\text{sert into the formula:} \\ m\text{ = }\frac{-5-5}{8-0} \\ m\text{ = }\frac{-10}{8} \end{gathered}[/tex][tex]\begin{gathered} m\text{ = }\frac{-5}{4} \\ \\ \text{Hence, the slope of the line is }\frac{-5}{4} \end{gathered}[/tex]
The y-intercept of a line is the value of y when x = 0
We will check the graph for the value of y when x = 0. This is also the point the line crosses the y axis.
The line crosses the y axis at y = 5
At this point, x = 0
Hence, the value of y of the y-intercept of the line shown is 5
The equation of line is given as:
y = mx + b
where m = slope
b = y-intercept
using the format above, our m = slope = -5/4
b = y-intercept = 5
inserting the values into the equation of line, the equation of line becomes:
[tex]y\text{ = }\frac{-5}{4}x\text{ + 5}[/tex]
