Question

Please I need help!

Write the equation of the line that passes through the points (7, -4) and ( 1, 3), first in point-slope form, and then in
slope intercept form
The slope of the line is
When the point (7, -4) is used, the point-stope form of the line is
The slope intercept form of the line is

Answer 1

Answer: Shown Below

Explanation:

1. -7/8

2. y+4= (-7/8)(x-7)

3. y=(-7/8)x+ (17/8)

Just did it

Answer 2

1)

`\text{ Slope = -3}`

2)

`y+4=-(7)/(8)(x-7)`

3)

`y=-(7)/(8)x+(17)/(8)`

Explanation:

We want to write the equation of the line that passes through the points (7, -4) and (-1, 3) first in point-slope form and then in slope-intercept form.

1)

First and foremost, we will need to find the slope of the line. So, we can use the slope-formula:

`m=(y_2-y_1)/(x_2-x_1)`

Let (7, -4) be (x₁, y₁) and let (-1, 3) be (x₂, y₂). Substitute them into our slope formula. This yields:

`m=(3-(-4))/(-1-7)`

Subtract. So, our slope is:

`m=(7)/(-8)=-7/8`

2)

Now, let's use the point-slope form:

`y-y_1=m(x-x_1)`

We will substitute -7/8 for our slope m. We will also use the point (7, -4) and this will be our (x₁, y₁). So, substituting these values yield:

`y-(-4)=-(7)/(8)(x-7)`

Simplify. So, our point-slope equation is:

`y+4=-(7)/(8)(x-7)`

3)

Finally, we want to convert this into slope-intercept form. So, let's solve for our y.

On the right, distribute:

`y+4=-(7)/(8)x+(49)/(8)`

Subtract 4 from both sides. Note that we can write 4 using a common denominator of 8, so 4 is 32/8. This yields:

`y=-(7)/(8)x+(49)/(8)-(32)/(8)`

Subtract. So, our slope-intercept equation is:

`y=-(7)/(8)x+(17)/(8)`

And we're done!