Question

Write the inequality for the graph.use the two points shown

Answer 1

Answer:

The inequality for the graph is y > -2x + 7 ⇒ A

Step-by-step explanation:

At first let us find the equation of the line, then write the inequality

∵ The form of the equation of the line is y = m x + b, where m is the slope

   and b is the y-intercept (value x at y = 0)

∵ m = $\frac{y2-y1}{x2-x1}$ , (x1, y1) and (x2, y2) are 2 points on the line

∵ The line passes through points (3, 1) and (0, 7)

∴ x1 = 3, y1 = 1 and x2 = 0, y2 = 7

→ Substitute them in the rule of the slope above

∵ m = $\frac{7-1}{0-3}$ = $\frac{6}{-3}$ = -2

∴ m = -2

→ Substitute it in the form of the equation

∴ y = -2x + b

∵ b is the value of y at x = 0

∵ y = 7 at x = 0

∴ b = 7

→ Substitute it in the equation

∴ y = -2x + 7

→ Now let us write the inequality

∵ The line is a dashed line and the shading is above the line

∴ The sign of inequality is >

→ Change "=" in the equation of the line by ">"

∴ The inequality is y > -2x + 7