Find the equation of the line that passes through the points (1, 2) and (-4, 3).
We can write an equation of a line in point-slope form: y - y1 = m(x - x1), where m is the slope of the line, and (x1, y1) are coordinates of a point on the line. Since we are given two points, we can pick either of these points to use for our x1 and y1 values. I am going to use the point (1, 2). So x1 = 1, y1 = 2. The only remaining piece of information we need to find is the slope of the line. To find slope of a line, we can use the formula: (y2 - y1)/(x2 - x1). Since I have already designated x1, y1, I will assign x2 and y2 to the values from the other point. So x2 = -4, and y2 = 3. Substituting all of the values into the equation, we get: (3 - 2)/(-4 - 1) = 1/-5. So our slope, m, = -1/5 Now we have enough information to write out the equation of the line by substituting in our values for m, x1, and y1: y - 2 = -1/5 (x - 1)
Explain how the short story "The Necklace" by Guy de Maupassant illustrates an example of situational irony.
In the shorty story "The Necklace", the main character Mathilde loses a precious pearl necklace that she had borrowed from a friend. Mathilde spends all her money and goes into debt for the rest of her life in order to afford replacing the necklace without her friend knowing. At the end of the story, Mathilde happens to run into her friend after years of no contact, and finally tells her friend the truth about losing the necklace. From the conversation that follows, the reader learns that the original necklace was not made from real pearls, but merely from paste. This unexpected twist of events demonstrates an example of situational irony.
Solve the following equation for x: 2x + 3(x - 3) = 6
Step 1: Use the distribution property to multiply 3 by both terms inside the brackets 2x + 3x - 9 = 6 Step 2: Add the "like terms" of 2x and 3x 5x - 9 = 6 Step 3: Add 9 to both sides of the equation 5x = 15 Step 4: Divide both sides of the equation by 5 to isolate x. x = 3