Answer:
- (x, y) = (19, 73)
- (x, y) = (-1, -97)
- (x, y) = (11 4/17, 7)
Step-by-step explanation:
You are given a point and a slope, so you can write the linear equation relating x and y using the point-slope form of the equation for a line. That form for slope m and point (h, k) is ...
y = m(x -h) +k
For your given values, m = 8.5, and (h, k) = (11, 5), the equation relating x and y can be written ...
y = 8.5(x -11) +5
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Evaluating this for several different x-values can be done with a spreadsheet or calculator. I like to write the function into a graphing calculator and let it do the tedious arithmetic. (See the attachment.)
However, to show you what is involved in doing this by hand, we can ...
let x = 19, then ...
y = 8.5(19 -11) +5 = 8.5·8 +5 = 73
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let x = -1, then ...
y = 8.5(-1-11) +5 = 8.5·(-12) +5 = -97
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To find the value of x for y=7, we can realize that to make y go up by 2 (from the given point of 5), we need to have x go up by 2/8.5 (from the given point of 11). That is ...
for y = 7 ...
x = 11 + 2/8.5 = 11 + 4/17 = 11 4/17
