Write the equation of the line that passes through the points (8,4) and (−9,6). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
First, let's find the slope of the line using the formula:
m = (y2 - y1)/(x2 - x1)
Using the points (8,4) and (-9,6):
m = (6 - 4)/(-9 - 8)
m = 2/-17
Now, let's choose one of the points to use in the point-slope form equation.
Let's choose (8,4).
Using the point-slope form y - y1 = m(x - x1):
y - 4 = (2/-17)(x - 8)
Multiplying both sides by -17 to eliminate the fraction:
-17(y - 4) = 2(x - 8)
Simplifying:
-17y + 68 = 2x - 16
Rearranging to have the equation in standard form:
2x + 17y = 84
Therefore, the equation of the line that passes through the points (8,4) and (-9,6) is 2x + 17y = 84 in standard form.
what is the point slope form
The point-slope form of a linear equation is:
y - y1 = m(x - x1),
where (x1, y1) is a point on the line and m is the slope of the line.
Using the slope of -2/17 and the point (8,4), the equation in point-slope form becomes:
y - 4 = (-2/17)(x - 8)