The slope of line is [tex]\frac{-7}{8}[/tex]
The point slope form is found when point (7, -4) is used is [tex]y + 4 = \frac{-7}{8}(x - 7)[/tex]
The slope intercept form is [tex]y = \frac{-7}{8}x + \frac{17}{8}[/tex]
Solution:
We have to find the equation of the line that passes through the points 7, -4 and -1, 3
The point slope form is given as:
[tex]y - y_1 = m(x - x_1)[/tex]
Where "m" is the slope of line
Given two points are (7, -4) and (-1, 3)
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Substituting [tex](x_1 , y_1 ) = (7, -4) \text{ and } (x_2, y_2) = (-1, 3)[/tex]
[tex]m=\frac{3-(-4)}{-1-7}=\frac{7}{-8}[/tex]
[tex]m=\frac{-7}{8}[/tex]
Thus slope of line is found
Substitute value of m and point (7, -4) in eqn 1
[tex]y - (-4) = \frac{-7}{8}(x - 7)\\\\y + 4 = \frac{-7}{8}(x - 7)[/tex]
Thus the point slope form is found when point (7, -4) is used
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
[tex]-4 = \frac{-7}{8}(7) + c\\\\-32 = -49 + 8c\\\\8c = 17\\\\c = \frac{17}{8}[/tex]
Substitute m = -7/8 and [tex]c = \frac{17}{8}[/tex] in eqn 1
[tex]y = \frac{-7}{8}x + \frac{17}{8}[/tex]
Thus the required equation of line is found
Answer:
Quick Answer
1. -7/8
2. y+4= (-7/8)(x-7)
3. y=(-7/8)x+(17/8)
Step-by-step explanation:
I just answered this on edg.
