Tutor profile: Karen M.
Find the slope and y-intercept of the line that is parallel to 2x + 3y = 5 and passes through the point (1, −1)
To solve for the slope, you must first get the equation in terms of y, that is, getting the y alone. Therefore you would subtract 2x on both sides of the equation to get 3y=5-2x, and then divide by 3 to get the y alone which gets you to y=(5-2x)/3. After doing this, we know the slope has to be the number 2/3, and since a parallel line is supposed to follow in the same direction and have the same slope, the slope of the parallel line would also be 2/3. At this point, we have to use the point-slope formula (y-y1)=m(x-x1) to find the equation of the line that passes through (1, -1). Plug that point and the slope into the formula (y-(-1))=2/3(x-1) which equals y+1=(2/3)x-(2/3). Once simplified to get the y alone, you would subtract the 1 from both sides of the equation and get y=(2/3)x-(2/3)-1 which is y=(2/3)x-(5/3).
Subject: Basic Math
Here, you must distribute the negative to whatever is in the parenthesis. Treat it like you have -1 times (3ab+4ac-(-2b)). -1 times 3ab equals -3ab because a negative times a positive gives you a negative. -1 times 4ac equals -4ac by the same principle. -1 times -2b equals 2b based on the idea that a negative times a negative equals a positive. Therefore, the answer to this equation is -3ab-4ac+2b.
A father gave $500 to his two sons. He gave X dollars to one son. What expression correctly shows the amount he gave to the other?
$500-x represents the amount the father gave to the other son. We know he has $500 and has to give x amount to one son. Taking that x amount away from the total gives the expression I listed.
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