After observing this pattern, Lexie made a conjecture for the next shape in the pattern. Five squares in a row. Each square has
a segment extending from its center to a vertex of the square. In the first square, the segment extends to the top left. In the second square, the segment extends to the top right. In the third square, the segment extends to the bottom right. In the fourth square, the segment extends to the bottom left. In the fifth square, the segment extends to the top left. Which shape was most likely her conjecture for the next shape?
2 answers:
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Part 1: The equation of the line is
Part 2: The equation of the line in slope intercept form is
Explanation:
Part 1: It is given that the point A is and the line B is
To determine the line passing through the point A and parallel to line B, let us first determine the slope and y-intercept.
From the equation of line B, the slope is
Substituting the point and
in slope intercept form
, we have,
Thus, the y-intercept is
Let us substitute the values and
in the slope intercept form
, we get,
Thus, the equation of the line passing though point A and parallel to line B is
Part 2: The given two coordinates are and
To determine the equation of line in slope intercept form, first we shall find the slope and y-intercept.
From the graph, we can see that the line touches the y-axis at -1.
Hence, the y-intercept is
The formula for slope is
Substituting the coordinates and
, we have,
Thus, the slope is
Substituting the values and
in the slope intercept formula
, we get,
Thus, the equation of the line in slope intercept form is