Alex drew a scale drawing of an auditorium. He used the scale 3 inches = 2 feet. If the stage is 30 inches in the drawing, how w
1 answer:
Answer:
20 feet
Step-by-step explanation:
The scale is 3 inches is to 2 feet
As a ratio, it would be:
The question is what is the actual length of the stage if the drawing is 30 inches. All we need to do is find a ratio proportional to the scale ratio:
Now to find the missing number, cross multiply the fractions first:
Then solve for x:
The answer is 20 feet
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Answer:
y = 3x +2
Step-by-step explanation:
It is helpful to be acquainted with the parts of at least a couple of different forms of the equation for a line.
You are given the equation of a line in "slope-intercept" form. It looks like ...
... y = mx + b . . . . . . . where m=-1/3 and b=-1
The coefficient of x, which is m, is the slope of the line. That is -1/3 for the given line.
The relationship between the slopes of perpendicular lines is that they multiply to give -1. We say each is the opposite reciprocal of the other. If we let "m" stand for the slope of the perpendicular line, it satisfies the equation ...
...(m)(-1/3) = -1
... m = -1/(-1/3) = 3 . . . . . the slope of the perpendicular line is 3.
____
Here's where another form of the equation for a line is useful. We can write the "point-slope" form* as ...
... y = m(x -h) +k . . . . . . for a line of slope m through point (h, k)
We want our line of slope = 3 to go through the point (1, 5), so its equation can be ...
... y = 3(x -1) +5 . . . . . . . variation of "point-slope" form
The given equation is in slope-intercept form, and the question asks for "the" equation of the line, so we probably should write our answer in the same form as the given equation. We can do this by eliminating the parentheses and simplifying the equation we have.
... y = 3x -3 +5 . . . . eliminate parentheses using the distributive property
... y = 3x +2 . . . . . . collect terms
The graph shows our result is at least plausible: it looks like it is perpendicular, and it goes through the given point.
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<em>*Comment on point-slope form</em>
Usually, you will see "point-slope" form written as ...
... y -k = m(x -h) . . . . . . . . standard version of "point-slope" form
When our intent is to use this form to get to slope-intercept form, it is more convenient to add k to this equation to get ...
... y = m(x -h) +k . . . . . . . occasionally useful version
