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

The slope of line is $\frac{-7}{8}$

The point slope form is found when point (7, -4) is used is $y + 4 = \frac{-7}{8}(x - 7)$

The slope intercept form is $y = \frac{-7}{8}x + \frac{17}{8}$

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

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

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

$m=\frac{3-(-4)}{-1-7}=\frac{7}{-8}$

$m=\frac{-7}{8}$

Thus slope of line is found

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

$y - (-4) = \frac{-7}{8}(x - 7)\\\\y + 4 = \frac{-7}{8}(x - 7)$

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

$-4 = \frac{-7}{8}(7) + c\\\\-32 = -49 + 8c\\\\8c = 17\\\\c = \frac{17}{8}$

Substitute m = -7/8 and $c = \frac{17}{8}$ in eqn 1

$y = \frac{-7}{8}x + \frac{17}{8}$

Thus the required equation of line is found

Answer 2

Answer:

Quick Answer

1. -7/8

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

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

Step-by-step explanation:

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