Question

review section.

1. google to learn! graph the line.

$y=-3x + 2$

1. what is the inverse of the following conditional?

if a cat is happy, then it is purring.

1. use the law of syllogism to reach a conclusion.

if $\angle 2$ is acute, then $\angle 3$ is obtuse. if $\angle 3$ is obtuse, then $\angle 4$ is acute.

Explanation:

11. Graphing the line \(y = - 3x+2\)

Step1: Find the y - intercept

The equation of a line is in the form \(y=mx + b\), where \(b\) is the y - intercept. For \(y=-3x + 2\), when \(x = 0\), \(y=2\). So, one point on the line is \((0,2)\).

Step2: Find another point using the slope

The slope \(m=-3=\frac{\Delta y}{\Delta x}\). From the point \((0,2)\), if \(\Delta x = 1\), then \(\Delta y=-3\). So, another point is \((0 + 1,2-3)=(1,-1)\).

Step3: Plot the points and draw the line

Plot the points \((0,2)\) and \((1,-1)\) on the coordinate grid and draw a straight line passing through them.

12. Finding the inverse of the conditional statement

A conditional statement is of the form “If \(p\), then \(q\)”. The inverse is “If not \(p\), then not \(q\)”. Here, \(p=\)“a cat is happy” and \(q=\)“it is purring”.

The Law of Syllogism states that if \(p
ightarrow q\) and \(q
ightarrow r\), then \(p
ightarrow r\). Here, \(p = \angle2\) is acute, \(q=\angle3\) is obtuse, \(r=\angle4\) is acute.

Answer:

If a cat is not happy, then it is not purring.

13. Using the Law of Syllogism