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in Geometry and Algebra by (30.8k points)
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a. Find the slope of the line joining the points (5, 3) and (4, 1).

b. Which are the points where this line meets x-axis and y-axis?

c. Write the coordinates of two other points on the line.

1 Answer

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a. Let (5, 3) = (x1, y1) and (4, 1) = (x2, y2), = slop

\(\frac{y_2-y_1}{x_2-x_1}=\frac{1-3}{4-5}=\frac{-2}{-1}=\frac{2}{1}=2\)

b. If the line meets x axis at the point (x, 0), then slope = \(\frac{a-3}{x-5}=2\)

\(\Rightarrow\) \(2(x-5)=-3\)

2x – 10 = –3,

2x = –3 + 10 = 7,

x = 7/2 = 3.5,

point is = (3.5, 0)

y axis \(\frac{y-3}{0-5}=2\) point (0, -7)

c. slope is (2/1) means when x coordinate increase/decreases by 1, y co-ordinate increases decreases by 2. Another point on 

the line is (5 + 1), (3 + 2) = (6, 5) 

A third point = (6 + 1) (5 + 2) = (7, 7)

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