Question

Find the equation of the line that goes through the points (4, –1) and (2, –5).

Use slope formula,m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction,to find the slope of a line that passes through the points.
m =
Use slope-intercept form, y = mx + b, to find the y-intercept (b) of the line.
b =
Write the equation in slope-intercept form, y = mx + b.

Answer 1

y= 2x -9

Explanation:

Slope-intercept form

y= mx +c, where m is the slope and c is the y-intercept.

`\boxed{slope = ( y_(1) - y_2)/(x_1 - x_(2)) }`

Slope

`= ( - 1 - ( - 5))/(4 - 2)`

`= ( - 1 + 5)/(2)`

`= (4)/(2)`

= 2

Substitute m= 2 into the equation:

y= 2x +c

To find the value of c, substitute a pair of coordinates.

When x= 4, y= -1,

-1= 2(4) +c

-1= 8 +c

c= -1 -8

c= -9

Thus, the equation of the line is y= 2x -9.