Question

write the equation of the line that passes through the points 7, -4 and -1, 3 first and point-slope form and then in slope intercept form. The slope of the line is? When the point 7, -4 is used, the point of the slope form of the line is? The slope intercept form of the line is?

Answer 1

Quick Answer

1. -7/8

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

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

Explanation:

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Answer 2

The slope of line is
`(-7)/(8)`

The point slope form is found when point (7, -4) is used is
`y + 4 = (-7)/(8)(x - 7)`

The slope intercept form is
`y = (-7)/(8)x + (17)/(8)`

Solution:

We have to find the equation of the line that passes through the points 7, -4 and -1, 3

Point slope form:

The point slope form is given as:

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

Where "m" is the slope of line

Given two points are (7, -4) and (-1, 3)

Let us find the slope of line

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

Substituting
`(x_1 , y_1 ) = (7, -4) \text{ and } (x_2, y_2) = (-1, 3)`

`m=(3-(-4))/(-1-7)=(7)/(-8)`

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

Thus slope of line is found

Substitute value of m and point (7, -4) in eqn 1

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

Thus the point slope form is found when point (7, -4) is used

Slope intercept form:

The slope intercept form is given as:

y = mx + c ----- eqn 1

Where "m" is the slope of line and "c" is the y - intercept

Substitute m = -7/8 and (x, y) = (7, -4) in eqn 1

`-4 = (-7)/(8)(7) + c\\\\-32 = -49 + 8c\\\\8c = 17\\\\c = (17)/(8)`

Substitute m = -7/8 and
`c = (17)/(8)` in eqn 1

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

Thus the required equation of line is found