Answer:
Y = 3X + 12
Explanation:
You are given several points on the line, so you can use a couple of them to find the slope, then write the equation in point-slope form and rearrange it to the desired form.
... slope = (change in Y)/(change in X)
Using the first two points, this is ...
... slope = (69 -51)/(19 -13) = 18/6 = 3
Point-Slope Form
The point-slope form of the equation of a line is usually written ...
... y -y1 = m(x -x1) . . . . . . where m = slope, (x1, y1) = point
This can be put into a y= form by adding y1:
... y = m(x -x1) +y1
Your Equation
Filling in m=3, (x1, y1) = (13, 51), the equation becomes
... y = 3(x -13) +51
... y = 3x -39 +51 . . . . . eliminate parentheses
... y = 3x +12 . . . . . . . . . simplify to slope-intercept form
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Alternate Solution
Having found the slope to be 3, you can write the slope-intercept form and fill in what you know.
... y = mx + b . . . . . slope-intercept form
... 51 = 3·13 +b . . . . slope-intercept form with slope and first point filled in
... 51 -39 = b = 12 . . . . equation solved for b by subtracting 39
Now you know that the equation is
... y = 3x +12
