Question

1. match the following
2. for linear inequalities, if its > or ≥ then shade ___ the line.

a. dotted

1. for linear inequalities, if its < or > then use ___ a line.

b. below
c. solid
d. above

1. find the slope of the line that goes through the points (-1, 2) and (6, -4). show all your work.

Explanation:

Question 1 and 2 (Matching)

1. For linear inequalities, the rule for shading: when the inequality is \(>\) or \(\geq\), we shade above the line. So we match with option d. For the line type: when the inequality is \(<\) or \(>\) (strict inequalities), we use a dotted line (option a), and when it's \(\leq\) or \(\geq\) (non - strict), we use a solid line. Wait, no, let's re - check:

• For shading: If the inequality is \(y > mx + b\) or \(y\geq mx + b\), we shade above the line. If it's \(y\) or \(\geq\), we shade above (d).
• For the line style: If the inequality is strict (\(<\) or \(>\)), we use a dotted line (because the points on the line are not included). If it's non - strict (\(\leq\) or \(\geq\)), we use a solid line (because the points on the line are included). So for question 2, since it's \(<\) or \(>\) (strict), we use a dotted line (a). Wait, no, the options:
• Option a: dotted; option b: below; option c: solid; option d: above.
• Question 1: "For linear inequalities, if it's \(>\) or \(\geq\) then shade ___ the line." The correct answer is d (above).
• Question 2: "For linear inequalities, if it's \(<\) or \(>\) then use ___ a line." The correct answer is a (dotted), because strict inequalities do not include the line, so we use a dotted line.

Step 1: Recall the slope formula

The slope \(m\) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Step 2: Identify the points

We are given the points \((-1,2)\) and \((6,-4)\). So, \(x_1=-1\), \(y_1 = 2\), \(x_2=6\), and \(y_2=-4\).

Step 3: Substitute the values into the formula

Substitute the values into the slope formula: \(m=\frac{-4 - 2}{6-(-1)}\).
First, calculate the numerator: \(-4 - 2=-6\).
Then, calculate the denominator: \(6-(-1)=6 + 1 = 7\).
So, \(m=\frac{-6}{7}\).

Answer:

1. d. above
2. a. dotted

Question 4 (Finding Slope)