Question

Write the slope-intercept form of the equation of the line through the given points.

through: (1,2) and (0,-4)
A) y=−6x+2
B) y=−6x−4
C) y=6x+2
D) y=6x−4

through: (4,-2) and (-5,1)
A) y= 3/9 x−2
B) y=− 3/9 x−2
C) y= 3/9 x+2
D) y=− 3/9 x+2

Answer 1

To find the slope-intercept form of the equation of a line through two given points, we need to find the slope and the y-intercept. We can use the formula for slope (m) and y-intercept (b) to find the equation of the line.

Step-by-step explanation:

To find the slope-intercept form of the equation of a line through two given points, we need to find the slope and the y-intercept.

The slope (m) can be found using the formula:

m = (y2 - y1)/(x2 - x1)

The y-intercept (b) can be found using the formula:

b = y - mx

Once we have the slope and y-intercept, we can plug them into the equation y = mx + b to get the slope-intercept form.

For the first set of points (1,2) and (0,-4):

Slope (m) = (-4 - 2)/(0 - 1) = -6

Using one of the points, we can find the y-intercept (b):

2 = -6(1) + b

b = 8

Therefore, the equation of the line is y = -6x + 8.

For the second set of points (4,-2) and (-5,1):

Slope (m) = (1 - (-2))/(-5 - 4) = 3/9 = 1/3

Using one of the points, we can find the y-intercept (b):

-2 = (1/3)(4) + b

b = -8/3

Therefore, the equation of the line is y = 1/3x - 8/3.