Answer:
The answers are:
[tex]Slope = m = -2\\y-intercept = b = 2[/tex]
New equation of line => [tex]y = -2x+2[/tex]
Step-by-step explanation:
Given points are:
[tex](x_1,y_1) = (-3,8)\\(x_2,y_2) = (4,-6)[/tex]
As the formula for slope is given as:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Putting the values
[tex]m = \frac{-6-8}{4-(-3)}\\m = \frac{-14}{4+3}\\= \frac{-14}{7}\\=-2[/tex]
So,
m = -2
The slope-intercept form of equation of line is given by:
[tex]y = mx+b[/tex]
Here m is the slope of the line and (x,y) are the coordinates of any point on the line.
As the line passes through both given points, one of the points and slope of line can be used to find the y-intercept of line.
Using the point (-3,8)
[tex]8 = -2(-3) + b\\8 = 6 + b[/tex]
Subtracting 6 from both sides
[tex]8-6 = 6+b-6\\2 = b[/tex]
To get the new equation of line, value of slope and y-intercept will be used:
Putting the values of b and m in slope-intercept form
[tex]y = mx+b\\y = -2x+2[/tex]
Hence
[tex]Slope = m = -2\\y-intercept = b = 2[/tex]
New equation of line => [tex]y = -2x+2[/tex]
