Question

A line contains the points (4,2) and (0, -1).What is the equation of the line?

Answer 1

Answer: y = - 3x/4 + 5

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis represent

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

The line passes through (4,2) and (0, - 1),

y2 = - 1

y1 = 2

x2 = 0

x1 = 4

Slope,m = (2 - - 1)/(0 - 4) = - 3/4

To determine the y intercept, we would substitute x = 4, y = 2 and m= - 3/4 into

y = mx + c. It becomes

2 = - 3/4 × 4 + c

2 = - 3 + c

c = 2 + 3 = 5

The equation becomes

y = - 3x/4 + 5

Answer 2

Find the slope:

y₂ - y₁ / x₂ - x₁

-1 - 2 / 0 - 4

-3 / -4

3/4

y = mx + b

y = 3/4x + b

Substitute any of the point's coordinate in the equation.

I'll pick (0,-1)

y = 3/4x + b

-1 = 3/4(0) + b

-1 = 0 + b

-1 = b

y-intercept = -1

y-intercept Equation:

y = 3/4x - 1

Point-slope form:

y - 2 = 3/4(x - 4)

Standard form:

-3/4x + y = -1