Answer:
[tex]y = -\frac{5}{4} x+5[/tex]
Step-by-step explanation:
1) First, find the slope of the line by using two points on the graph. We can see that (0,5) and (4,0) are clearly marked on the line, so let's use those points. Use the slope formula [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex] and substitute the x and y values of those points into it, then simplify:
[tex]m =\frac{0-5}{4-0} \\m = \frac{-5}{4}[/tex]
So, the slope is [tex]-\frac{5}{4}[/tex].
2) Now, identify the y-intercept on the graph. The y-intercept is the point at which the line intersects the y-axis. By reading the graph, we can see that the line intersects the y-axis at (0,5), so that must be the y-intercept.
3) Substitute values for [tex]m[/tex] and [tex]b[/tex] in the slope-intercept formula, [tex]y = mx + b[/tex], to write the equation of the line. Since [tex]m[/tex] represents the slope, substitute [tex]-\frac{5}{4}[/tex] for it. Since [tex]b[/tex] represents the y-intercept, substitute 5 in its place. This gives the following answer and equation in slope-intercept form:
[tex]y = -\frac{5}{4} x+5[/tex]
