Answer:
[tex]y=\frac{-3}{7}x+\frac{15}{7}[/tex]
Step-by-step explanation:
To determine the equation of the line graphed, first you will need to determine the slope of the line. To do this, pick two points that the line intersects, such as (5,0) and (-2,3). Now determine the change in the x and y coordinates for these points.
Change in y-coordinates:
0-3=-3
Change in x-coordinates:
5-(-2)=5+2=7
The slope is equal to the change in the y-coordinates divided by the change in the x-coordinates.
Calculating slope:
[tex]m=\frac{-3}{7}[/tex]
Now that the slope has been found, look at the graph to determine the y-intercept. On this graph the function intersects the y-axis between y=2 and y=3. Rearrange the slope intercept equation to solve for the y-intercept.
Rearranging y=mx+b for b:
b=y-mx
Plugging (5,0) into the rearranged equation:
[tex]b=0-\frac{-3}{7} *5=\frac{3}{7}*5=\frac{15}{7}[/tex]
Now that the slope and y-intercept have been calculated, the equation for this function can be written by plugging both of these into slope intercept form.
[tex]y=mx+b[/tex]
[tex]y=\frac{-3}{7}x+\frac{15}{7}[/tex]
