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 = [tex]\frac{y2-y1}{x2-x1}[/tex] , (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 = [tex]\frac{7-1}{0-3}[/tex] = [tex]\frac{6}{-3}[/tex] = -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
