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3 years ago

Find the equation of a line which has 10 points the following two coordinates: (4, 0) and (3, 4)

alex41 [277]

Answer:

The equation of the line is y = -4·x + 16

10 points on the line include;

(0, 16), (1, 12), (2, 8), (3, 4), (4, 0), (5, -4), (6, -8), (7, 12), (8, -16), (9, -20), and (10, -24)

Explanation:

The given points through which the line passes are;

(4, 0) and (3, 4)

The slope, 'm', of the line is given as follows;

$Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Therefore, the slope of the line is (4 - 0)/(3 - 4) = -4

In point and slope form we can get;

$\dfrac{y-0}{x-4} = -4$

The equation of the line in point and slope form is therefore;

y = -4·(x - 4) = -4·x + 16

The equation of the line in slope and intercept form is

y = -4·x + 16

10 points on the line are obtained using the equation of the line and the desired x-values input into cells on MS Excel and presented here as follows;

(0, 16), (1, 12), (2, 8), (3, 4), (4, 0), (5, -4), (6, -8), (7, 12), (8, -16), (9, -20), and (10, -24)