Question

Write an inequality to represent the graph. a dashed line passing through points 0 comma negative 3 and 2 comma 2 with shading above it

A.y is greater than two fifths times x minus 3 B. y is less than two fifths times x minus 3 C. y is greater than five halves times x minus 3 D. y is less than five halves times x minus 3

Answer 1

Answer: y > (5/2)*x - 3

Explanation:

Ok, the thins we should notice.

The line is shaded, so the values of the line are not solutions of the inequality, then we should use < or >.

The shaded part is above the line, so we have:

y > a*x + b.

A linear relationship can be written as:

f(x) = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

Now, we know that our line passes through the points (0, -3) and (2, 2)

Then the slope is:

a = (2 -(-3))/(2 - 0) = 5/2.

f(x) = (5/2)*x + b.

To find the value of b, we can replace the values of one of the points in the equation, let's use the point (0, -3)

f(0) = -3 = (5/2)*0 + b

-3 = b

Then the line is:

f(x) = (5/2)*x - 3

Then the inequality is:

y > (5/2)*x - 3