As given by the question
There are given that the graph of the line.
Now,
To find the slope and y-intercept of the line, first select two intersect point from the graph.
Then,
The points are:
[tex](0,\text{ 5) and (5, 0)}[/tex]
Then,
First find the slope,
So,
From the formula of slope,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where,
[tex]x_1=0,y_1=5,x_2=5,y_2=0[/tex]
Then,
Put all the value into the given formula.
So,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{0_{}-5_{}}{5_{}-0_{}} \\ m=-\frac{5}{5} \\ m=-1 \end{gathered}[/tex]
Now,
From the standard form of the line,
[tex]y=mx+b[/tex]
Then,
Put y is 5, x is 0 and m is -5 into the above equation to find the y-intercept
So,
[tex]\begin{gathered} y=mx+b \\ 5=-1(0)+b \\ b=5 \end{gathered}[/tex]
Hence, the value of the y-intercept is 5.
Now,
The line equation is shown below:
[tex]\begin{gathered} y=mx+b \\ y=-1x+b \\ y=-x+5 \end{gathered}[/tex]
Hence, the slope of the line is -1, y-intercept of the line is 5 and the equation of line is y = -x + 5.
