Answer:
4. [tex]-4x+y=15[/tex]
Step-by-step explanation:
We have been given a graph of a linear function and we are asked to find the correct equation representing the relationship shown in the graph.
Since we know that the standard form of an equation is in form: [tex]Ax+By=C[/tex], where A, B and C are integers.
First of all we will find the slope of our line and write equation of line in slope-intercept form. Then we will change it into standard form.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{23-15}{2-0}[/tex]
[tex]m=\frac{8}{2}=4[/tex]
Slope of our line is 4. We can see that y-intercept (b) is 15. Now let us write equation of our line in slope-intercept form.
[tex]y=mx+b[/tex]
[tex]y=4x+15[/tex]
Now we will change our given equation into standard form by subtracting 4x from both sides of our equation.
[tex]-4x+y=4x+15-4x[/tex]
[tex]-4x+y=15[/tex]
Therefore, the equation [tex]-4x+y=15[/tex] represents the relationship shown in the graph in standard form and 4th option is the correct choice.
