Answer :
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Hello! In this question, we are trying to solve the equation of a line with the given coordinate points and provide the answer in slope-intercept form.
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Explanation:
We are given the points in the question:
- (13,-14)
- (11,6)
Slope-intercept form:
y = mx + b
Whereas:
- m = slope
- b = y-intercept
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Solve:
To find the equation of the line, we first must solve for the slope of the line.
We can solve for the slope by using the following formula (which equates to rise over run):
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Solve for the slope by plugging in the coordinates to the equation:
[tex]m=\frac{6-(-14)}{11-13} \\\\m = \frac{6+14}{11-13}\\\\m=\frac{20}{-2} =-10[/tex]
Now, we need to find our y-intercept, which we can do this by plugging in our slope and one of the coordinates into the slope-intercept formula and solve for b:
y = mx + b
Plug in the slope (-10) and one of the coordinates (11, 6):
6 = -10(11) + b
Solve for b:
6 = -110 + b
116 = b
Therefore, the equation of our line is y = -10x + 116
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Answer:
y = -10x + 116
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