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

Question

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

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1 month 2021-11-07T05:56:13+00:00 2 Answers 0 views 0

## Answers ( )

1. 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

2. 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