To find the equation of the line passing through two points, we first need to find the slope of the line.
Let's use the formula for slope:
\[m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\]
where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points.
Using the points (0, 8) and (6, -2), we have:
\[m = \frac{{-2 - 8}}{{6 - 0}} = \frac{{-10}}{{6}} = -\frac{5}{3}\]
Now, we can use the point-slope form of a linear equation given a slope \(m\) and a point \((x_1, y_1)\):
\[y - y_1 = m(x - x_1)\]
Using the point (0, 8):
\[y - 8 = -\frac{5}{3}(x - 0)\]
Simplifying, we get the equation in point-slope form as:
\[y - 8 = -\frac{5}{3}x\]
However, the question asks for the equation to be put in fully simplified point-slope form, unless it is a vertical or horizontal line. Since the given line is neither vertical nor horizontal, we can further simplify the equation.
Multiplying through by \(3\) to get rid of the fraction:
\[3(y - 8) = -5x\]
Distributing on the left side:
\[3y - 24 = -5x\]
Finally, rearranging the equation to be in slope-intercept form ( \(y = mx + b\) ):
\[3y = -5x + 24\]
Dividing through by \(3\):
\[y = -\frac{5}{3}x + \frac{24}{3} = -\frac{5}{3}x + 8\]
Therefore, the equation of the line passing through the points (0, 8) and (6, -2) is \(y = -\frac{5}{3}x + 8\).
Write the equation of the line that passes through the points (0, 8) and (6, -2). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
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