Question

the graph of a linear function is shown on the grid. which equation is best represented by this graph?

A) y + 2 = 7/5(x + 7)
B) y - 3 = 7/5 (x - 7)
C) y + 2 = 5/7(x + 7)
D) y - 2 = 5/7(x - 7)​

Answer 1

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Answer:

  D) y - 2 = 5/7(x - 7)​

Step-by-step explanation:

The point-slope form of the equation for a line is ...

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

The given answer choices are written in point-slope form, so we can see they expect the line to go through one of the points (-7, -2), (7, 3), or (7, 2). Of these, we note that only point (7, 2) is on the line. (eliminates choices A, B, C)

To confirm that choice D is the correct choice, we can look at the slope between the y-intercept of (0, -3) and the point (7, 2). That is ...

  m = (y2 -y1)/(x2 -x1)

  m = (2 -(-3))/(7 -0) = 5/7

So, the equation of the line is ...

  y -2 = 5/7(x -7)