Math  /  Geometry

Question\begin{tabular}{|l|l} & \\ \hline & (2,5)&(4,6)(2,5) \&(-4,-6) \end{tabular} a. Plot the above two points: b. Work out the midpoint: c. Work out the distance: d. Work out the linear equation:

Studdy Solution
Determine the linear equation of the line through the points using the slope-intercept form y=mx+by = mx + b.
First, calculate the slope mm:
m=y2y1x2x1 m = \frac{y_2 - y_1}{x_2 - x_1} m=6542 m = \frac{-6 - 5}{-4 - 2} m=116 m = \frac{-11}{-6} m=116 m = \frac{11}{6}
Use point-slope form yy1=m(xx1)y - y_1 = m(x - x_1) with point (2,5)(2, 5):
y5=116(x2) y - 5 = \frac{11}{6}(x - 2)
Convert to slope-intercept form:
y5=116x226 y - 5 = \frac{11}{6}x - \frac{22}{6} y=116x226+5 y = \frac{11}{6}x - \frac{22}{6} + 5 y=116x+86 y = \frac{11}{6}x + \frac{8}{6} y=116x+43 y = \frac{11}{6}x + \frac{4}{3}
The linear equation of the line through the points is:
y=116x+43 y = \frac{11}{6}x + \frac{4}{3}

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