Question

Which of the following inequalities matches the graph? Graph of an inequality with a solid line through the points (1, 4) and (2, 9) with shading below the line.

A. 5x + y greater than or equal to 1
B. 5x + y less than or greater to 1
C. 5x - y greater than or equal to 1

Answer 1

The inequality 5x - y greater than or equal to 1 matches the graph. The correct answer between all the choices given is the last choice or letter C. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

Answer 2

The equation of the generic line is:

$y-yo = m (x-xo)$

Where,

(xo, yo): ordered pair where the line passes

m: slope of the line

For the slope we have:

$m = \frac{y2-y1}{x2-x1}$

Substituting values:

$m = \frac{9-4}{2-1}$

$m = \frac{5}{1} m=5$

Then, we choose an ordered pair:

$(xo, yo) = (1, 4)$

Substituting values we have:

$y-4 = 5 (x-1)$

Rewriting we have:

$y = 5x-5 + 4 y = 5x-1 5x-y = 1$

Then, we know that the shaded region is below the line, so the inequation is:

$5x-y\geq 1$

Answer:

The following inequality matches the graph:

C. 5x - and greater than or equal to 1