Question

what equation, in point-slope form, matches the graph line shown?A: y - 2 = - 3/4 (x - 6)B: y + 6 = 4/5 ( x + 3) C: y - 5 = - 2/3 (x + 9) D: y - 6 = 4/5 (x - 2)

Answer 1

A line with slope m and that passes through the point (x₁, y₁) have the following point-slope form equation:

`y-y_1=m(x-x_1)`

Furthermore, if this line passes through a second point (x₂, y₂), its slope is given by:

`m=(y_2-y_1)/(x_2-x_1)`

In this problem, the given line passes through points (6, 2) and (10, -1). So, we have:

x₁ = 6

y₁ = 2

x₂ = 10

y₂ = -1

Then, using those values to find m, we obtain:

`m=(-1-2)/(10-6)=-(3)/(4)`

And the equation of the line, in point-slope form, is:

`y-2=-(3)/(4)(x-6_{})`

Therefore, option A is correct.