What is an equation in point-slope form for the line that passes through the points (4,−1)(4,−1) and (−3,4)(−3,4) ?
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Answer:
The inequality represented by the graph is y > x - 3
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
- m is the slope of the line
- b is the y-intercept
The rule of the slope is m = , where
- (x1, y1) and (x2, y2) are two points on the line
<em>To find the inequality represented by the graph, find at first the equation of the line</em>
∵ The line passes through points (0, -3) and (3, -2)
∴ x1 = 0 and y1 = -3
∴ x2 = 3 and y2 = -2
→ Substitute them in the rule of the slope above to find it
∵ m = =
=
∴ m =
→ Substitute it in the form of the equation above
∴ y = x + b
∵ b is the y-intercept ⇒ value y at x = 0
∵ y = -3 at x = 0
∴ b = -3
→ Substitute it in the equation
∴ y = x + -3
∴ y = x - 3
→ Let us change it to inequality
∵ The line is dashed
∵ The shading area is above the line
∴ The sign of inequality should be >
∴ y > x - 3
∴ The inequality represented by the graph is y > x - 3
