Hello!
The problem has asked that we write a point-slope equation of the line in the image above. Point-Slope Form uses the following formula:
y – [tex] y_{1} [/tex] = m(x – [tex] x_{1} [/tex])
In this case, M represents the slope while [tex] X_{1} [/tex] and [tex] Y_{1} [/tex] represent the corresponding X and Y values of any given point on the line.
We are given that the slope of the line is -[tex] \frac{5}{7} [/tex]. We also know that any given point on a graph takes the form (x,y). Based on the single point provided in the image above, we can determine that [tex]X_{1} [/tex] is equal to 6 and [tex]Y_{1} [/tex] is equal to 2. Now insert all known values into the point-slope formula above:
y – 2 = -[tex] \frac{5}{7} [/tex](x – 6)
We have now successfully created an equation based on the information given in the problem above. Looking at the four possible options, we can now come to the conclusion that the answer is C.
I hope this helps!
