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What is the slope of a line that passes through the points [tex]$(-3,-5)$[/tex] and [tex]$(1,7)$[/tex] in the [tex][tex]$xy$[/tex][/tex]-plane?

Choose one answer:
A. 6
B. 3
C. [tex]$\frac{1}{2}$[/tex]
D. -1

Sagot :

GinnyAnsweridn
Sure! Let's determine the slope of the line passing through the points [tex]\((-3, -5)\)[/tex] and [tex]\((1, 7)\)[/tex].

The slope [tex]\(m\)[/tex] of a line through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by the formula:

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

Here, our points are [tex]\((x_1, y_1) = (-3, -5)\)[/tex] and [tex]\((x_2, y_2) = (1, 7)\)[/tex].

So we substitute these into the formula:

[tex]\[ m = \frac{7 - (-5)}{1 - (-3)} \][/tex]

Simplify the numerator and the denominator:

[tex]\[ m = \frac{7 + 5}{1 + 3} \][/tex]

[tex]\[ m = \frac{12}{4} \][/tex]

[tex]\[ m = 3 \][/tex]

Therefore, the slope of the line passing through the points [tex]\((-3, -5)\)[/tex] and [tex]\((1, 7)\)[/tex] is [tex]\(3\)[/tex].

Hence, the correct answer is:
(B) 3
Wegnerkolmp2741oidn

Answer:

B. 3

Step-by-step explanation:

To find the slope of a line given two points, we use the slope formula

m = ( y2-y1)/(x2-x1)  where the point is given in the form (x,y).

m = (7- -5)/(1 --3)

   = (7+5)/(1+3)

   = 12/4

   = 3

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