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ahrayia [7]
3 years ago
14

Find an equation of the line that passes through the points (-5, -3) and (3, 1)

Mathematics
2 answers:
horsena [70]3 years ago
7 0

Answer:

x - 2y - 7 = 0

Step-by-step explanation:

To find the equation of a line that passes through (-5, -3) and (3,1)

All we need to do is to use the find the slope and then plug it into the straight line equation

straight line equation :   y -  y_{1}   =   m (x  -  x_{1})

x_{1} = -5     y_{1} = -3   x_{2} = 3   y_{2} = 1

 

m = slope =  y_{2}  -  y_{1}   /  x_{2}  -  x_{1}

                =   1 -(-3)  /   3 -(-5)

                 =4/8

                  =1/2

m=1/2

So, we can now plug in our value into  the equation;

y  -  y_{1}   =   m (x -  x_{1})

y - (-5) = \frac{1}{2} [x - (-3)]

y + 5 = \frac{1}{2}(x+3)

y +  5  =  \frac{x + 3}{2}

cross-multiply

2(y + 5) =   x + 3

2y + 10  =  x + 3

take 2y and 10 to the right-hand side of the equation;

x + 3 - 2y - 10  = 0

x - 2y - 7 = 0

Therefore the equation of the line is x - 2y - 7 = 0

Mkey [24]3 years ago
6 0

\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-3})\quad (\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-5)}}}\implies \cfrac{1+3}{3+5}\implies \cfrac{4}{8}\implies \cfrac{1}{2}

\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{\cfrac{1}{2}}[x-\stackrel{x_1}{(-5)}]\implies y+3=\cfrac{1}{2}(x+5) \\\\\\ y+3=\cfrac{1}{2}x+\cfrac{5}{2}\implies y=\cfrac{1}{2}x+\cfrac{5}{2}-3\implies y = \cfrac{1}{2}x-\cfrac{1}{2}

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Answer:

(1,41), (2,40), (3,39), (4,38), (5,37), (6,36), (7,35), (8,34), (9,33), (10,32), (11,31), (12,30), (13,29), (14,28), (15,27), (16,26), (17,25), (18,24), (19,23), (20,22), (21,21), (22,20), (23,19), (24,18), (25,17), (26,16), (27,15), (28,14), (29,13), (30,12), (31,11), (32,10), (33,9), (34,8), (35,7), (36,6), (37,5), (38,4), (39,3), (40,2), (41,1).

Step-by-step explanation:

To find all pairs of natural numbers which are solution to a+b=42, we need to first choose a value to one of them (let's choose 'a'), and that value will be the lowest possible, so we begin with a=1, and then we increase to 2, and 3, and so on.

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So, starting with a=1, we have that b=41

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Doing this until a=41 (so b=1 will be the lowest value possible for b), we have the pairs of natural number we want:

(1,41), (2,40), (3,39), (4,38), (5,37), (6,36), (7,35), (8,34), (9,33), (10,32), (11,31), (12,30), (13,29), (14,28), (15,27), (16,26), (17,25), (18,24), (19,23), (20,22), (21,21), (22,20), (23,19), (24,18), (25,17), (26,16), (27,15), (28,14), (29,13), (30,12), (31,11), (32,10), (33,9), (34,8), (35,7), (36,6), (37,5), (38,4), (39,3), (40,2), (41,1).

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