Question

A line contains the points (4,2) and (0,-1). what is the equation of the line. a) y=2x -6

b)y= 3/4x -1
c) y= 1/4x + 1
d) y= 4/3x - 10/3

Answer 1

The equation of the line passing through the points (4,2) and (0,-1) is y = -3/4x + 5.

Step-by-step explanation:

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

The formula for finding the slope is: m = (y2 - y1) / (x2 - x1)

Using the points (4, 2) and (0, -1):

• x1 = 4, y1 = 2
• x2 = 0, y2 = -1

Substituting these values into the formula, we get: m = (-1 - 2) / (0 - 4) = 3 / -4 = -3/4

The slope of the line is -3/4.

Next, we can use the slope-intercept form of the equation of a line, which is: y = mx + b

Using one point and the slope, we can solve for the y-intercept, b.

• x = 4, y = 2, m = -3/4

Substituting these values into the slope-intercept form, we get: 2 = (-3/4)(4) + b

Simplifying this equation, we find: 2 = -3 + b

Adding 3 to both sides, we get: b = 5

Therefore, the equation of the line is: y = -3/4x + 5

Answer 2

To do this, we should calculate the gradient first
m=y2-y1 overx2-x1
m=-1-2 over 0-4
m=-3 over -4
m=3 over 4

formula of a straight is y-y1=m(x-x1)
y-2=3/4x-3
y=3/4x-1

so the answer is b)