write the equation of the line of the slope-intercept form

Question

A= -1,2 B= 0,-1

Answer 1

To find the equation of the line passing through points A(-1,2) and B(0,-1), we first need to find the slope of the line using the formula:

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

where (x1,y1) = (-1,2) and (x2,y2) = (0,-1)

m = (-1 - 2) / (0 - (-1))
m = (-1 - 2) / 1
m = -3

Now that we have the slope (m = -3), we can use one of the points and the slope to find the equation of the line in slope-intercept form (y = mx + b).
Let's use point A(-1,2):

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

Therefore, the equation of the line passing through points A(-1,2) and B(0,-1) in slope-intercept form is:
y = -3x - 1

Answer 2

derive the equation of the line y= mx through the origin
2,10 and 1,5

Answer 3

To derive the equation of the line y = mx passing through the origin and point (2,10) we need to calculate the slope and then write the equation in the form y = mx.

Given points: (2,10) and (1,5)

Calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (5 - 10) / (1 - 2)
m = -5 / -1
m = 5

Now that we have the slope (m = 5), we can write the equation of the line passing through the origin (0,0) and point (2,10) in the form y = mx.

Since the line passes through the origin, it has zero y-intercept (b = 0).

Therefore, the equation of the line is:
y = 5x