Respuesta :
The x-intercept of the line passing through the points (-6,10) and (12,-2) is 9
We have been given two coordinates which are,
(x1,y1) = (-6,10) and (x2,y2) = (12,-2)
To find the x-intercept, first we will form the equation of the line or write the slope-intercept form.
The slope-intercept form if two points are given is given as follows:
(y-y1) = m(x-x1) (1)
Where m = slope of the line
Formula to find the slope is, m= (y2-y1)/(x2-x1) (2)
Now putting the required coordinates in equation (2) we get
m = (-2-10)/(12+6)
m = -12/18
m = -2/3
Now we will put the value of slope in equation (1), we will get
(y-10) = -2/3(x+6)
(y-10) = -2/3x – 4
y = -2/3x -4 + 10
y = -2/3x + 6
which can also be written as 3y + 2x – 18 = 0 (3)
We have to the x-intercept, for which we will put y=0 in equation (3), that is
3(0) + 2x – 18 =0
2x = 18
x = 9
Hence the x-intercept is 9
Learn more about intercept here : https://brainly.com/question/24212383
#SPJ9
