Question

Write an equation in slope-intercept form for a line that passes through the given pair of points. (7, 2) (1, 0)

Answer 1

`y = \frac { 1 } { 3 }x - \frac { 1 } { 3 }`

Explanation:

We are given the points (7, 2) and (1, 0) and we are to find the equation of the line that passes through these points.

Slope =
`\frac { 2 - 0 } { 7 - 1 } = \frac { 2 } { 6 } = \frac { 1 } { 3 }`

Now that we have the slope, we will find the y-intercept:

`y = m x + c`

`0 = \frac { 1 } { 3 } ( 1 ) + c`

`c = - \frac { 1 } { 3 }`

So the equation will be:

`y = \frac { 1 } { 3 }x - \frac { 1 } { 3 }`

Answer 2

`y=(1)/(3)x-(1)/(3)`

Explanation:

THe slope intercept form of a line is y = mx + b

Where, m is the slope with formula
`m=(y_2-y_1)/(x_2-x_1)`

and

b is the y-intercept (the point where the line cuts the y-axis)

x_1 and y_1 is the first pair of points

x_2, y_2 is the second pair of points

Let's find m first by plugging in the points:

`m=(y_2-y_1)/(x_2-x_1)\\m=(0-2)/(1-7)\\m=(-2)/(-6)\\m=(1)/(3)`

Now we have y = 1/3x+b. We can plug in any point (let's use (1,0)) and find b:

`y=(1)/(3)x+b\\0=(1)/(3)(1)+b\\0=(1)/(3)+b\\b=-(1)/(3)`

THus, the equation of the line is
`y=(1)/(3)x-(1)/(3)`