Question

Write the slope-intercept inequality for the graph below (0,2)(-1,-2)

Answer 1

Given points say (x1,y1) = (0,2)

(x2,y2) = (-1,-2)

Equation of line  through the two points y-y1 = m(x-x1)

m = (-2-2)/(-1-0)

m = -4/-1

m = 4

y-2 = 4(x-0)

y = 4x+2

Compare slope intercept form is y = mx+c

m = 4, c = 2

From the graph we can observe the y ntercept is b = 2

slope is m = rise/run =change in y /change in x

= 2/0.5 = 4

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Answer 2

Let the points are (x₁, y₁) = (0, 2) and (x₂, y₂) = (- 1, - 2).

Slope m = [(y₂ - y₁)/(x₂ - x₁)]

m = [(- 2 - 2)/(- 1 - 0)]

m = - 4/- 1

⇒ m = 4.

Find the y - intercept by substituting any point in the line equation say (x, y) = (0, 2).

2 = 4 * 0 + b

⇒ b = 2.

Substitute the values of m = 4 and b = 2 in the slope - intercept form of equation.

y = mx + b

⇒ y = 4x + 2.

From the given data slope - intercept inequality for the graph below (0, 2) and (- 1, - 2) is

y < 4x + 2.

Graph of the inequality:

The graph of the inequality y < 4x + 2 symbol is <, the boundary is not included in the solutionset. Graph the boundary of the inequality y = 4x + 2 with dotted line.

1. Draw the coordinate plane.

2. To determine which half - plane to be shaded use a test point in either half - plane.

A simple choice is (0, 0).

Substitute x = 0 and y = 0 in the inequality y < 4x + 2.

0 < (4)0 + 2

0 < 2.

The above statement is true.

3. Since the statement is true, shade the region contains the point (0, 0).