Question

REVIEW: Find the slope for the following situations. a. Given the equation y = 5x + 1 b. Given the equation 2x + y = 6 c. Given the points: (2, 3) and (5, 9)

Answer 1

Answer:

Part 1) The slope is $m=5$

Part 2) The slope is $m=-2$

Part 3) The slope is $m=2$

Step-by-step explanation:

Part 1) we know that

The equation of the line into slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-coordinate of the y-intercept

In this problem we have

$y=5x+1$

so

the slope is $m=5$

Part 2) we know that

The equation of the line in standard form is equal to

$Ax+By=C$

where

the slope is equal to $m=-\frac{A}{B}$

in this problem we have

$2x+y=6$

so

$A=2,B=1,C=6$

substitute

$m=-\frac{2}{1}$

$m=-2$

Part 3) we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

$A(2,3)\ B(5,9)$

Substitute the values

$m=\frac{9-3}{5-2}$

$m=\frac{6}{3}$

$m=2$