Find the slope and y-intercept. Also, determine if it is Proportional or Non Proportional
1 answer:
Answer:
Step-by-step explanation:
Slope of a line passing through two points and
is,
m =
From the table attached,
Two points lying on the graph are (1, 12) and (2, 24).
Slope of the line will be,
m =
Slope = 12
Since equation of a line passing through a point (x', y') and slope 'm' is,
y - y' = m(x - x')
Therefore, equation of the line passing through (1, 12) and slope 12 will be,
y - 12 = 12(x - 1)
y = 12x - 12 + 12
y = 12x
By comparing this equation with the equation,
y = mx + b
where 'b' = y-intercept = 0
Since, y-intercept is zero, table will represent the proportional relation between x and y.
Proportional or non proportional → Proportional
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The sum of the triangular numbers is
According to the question, the series of triangular numbers is given as in the form of the number of dots constituting the equilateral triangles i.e.
1, 3, 6, 10, 15 . . . . .n
triangular number are the sequence and series of the numbers and each number represents and constitute in visualization of series of equilateral triangle.
given series in the figure
1, 3, 6, 10, 15, . . . . . . ., n
each number represents the number of dots containing in triangle
now the series can be given by
for n = 1, 2, 3, 4,. . . . .n
now , according to the question the sum of the series can be given as
⇒ ∑S
⇒ ∑
⇒
Thus, the sum of the triangular number is given by
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