Answer:
Step-by-step explanation:
The slope of a line can be found by determining [tex]\frac{rise}{run}[/tex], or for any two points on the line, [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex], using the equation, [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex].
From the given line, we can see two points on the graph are [tex](0, 5)[/tex] and [tex](2, 4)[/tex]. Plugging those into our equation, we get
[tex]\frac{4 - 5}{2 - 0}[/tex]
[tex]\frac{-1}{2}[/tex]
This means that the slope of the line is [tex]\frac{-1}{2}[/tex].
To find the y-intercept of the line, you need to find where the line crosses the y-axis, or where [tex]x = 0[/tex]. In this case, that is at point [tex](0, 5)[/tex].
Finally, to construct the equation for the line, you can use slope-intercept form, which follows the format
[tex]y = mx + b[/tex]
where [tex]m[/tex] is the slope of the line and [tex]b[/tex] is the y-intercept value.
Plugging in the values we retrieved previously, we can construct the equation for the line as follows:
[tex]y = \frac{-1}{2}x + 5[/tex]
