Interpret y = mx + b as defining a linear equation whose graph is a line with m as the slope and b as the y-intercept.

8.9.aUse similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in a coordinate plane.8.9.bGiven two distinct points in a coordinate plane, find the slope of the line containing the two points and explain why it will be the same for any two distinct points on the line.8.9.cGraph linear relationships, interpreting the slope as the rate of change of the graph and the y-intercept as the initial value.8.9.dGiven that the slopes for two different sets of points are equal, demonstrate that the linear equations that include those two sets of points may have different y-intercepts.
Example Problems
Write the equation of a line that is parallel to and that passes through the point .
Write the equation of a line that is perpendicular to and that passes through the point .
Write the equation of a line that is parallel to and that passes through the point .
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