step-by-step explanation:
the distance (d) between two points (x1,y1) and (x2,y2) is given by the formula
d = √ ((x2-x1)2+(y2-y1)2)
d = √ (-11-6)2+(4-3)2
d = √ )2+(1)2)
d = √ (289+1)
d = √ 290
the distance between the points is 17.0293863659264
the midpoint of two points is given by the formula
midpoint= ((x1+x2)/2,(y1+y2)/2)
find the x value of the midpoint
xm=(x1+x2)/2
xm=(6+-11)/2=-2.5
find the y value of the midpoint
ym=(y1+y2)/2
ym=(3+4)/2=3.5
the midpoint is: (-2.5,3.5)
graphing the two points, midpoint and distance
p1 (6,3)
p2 (-11,4)
midpoint (-2.5,3.5)
the length of the black line is the distance between the points (17.0293863659264)
find the slope of the line connecting the two points
slope = (y2-y1) = (4-3) = (1) = -0.0588235294117647
(x2-x1) (-11-6) (-17)
find the equation of the line passing through the two points
the general equation for a straight line is
y = mx + b
where m represents the slope of the line which we found in the previous step to be -0.0588235294117647
y = -0.06x + b
we substitute x and y for the values from one of our points (6,3)
3 = -.06×6 + b
3 = -0.35 + b
3--0.35 = b
3.35 = b
knowing both b and m, we can contruct the equation of the line
y= -0.06x+ 3.35
x and y intercepts
the x-intercept is a point on the graph where y is zero
using the equation we found in the previous step and substituting zero for y
y= -0.06x+ 3.35
0= -0.06x+ 3.35
0.06x= 3.35
x= 3.35/0.06 = 57.00
the x intercept for this straight line is 57.00
the y-intercept is a point on the graph where x is zero
using the equation we found in the previous step and substituting zero for x
y= -0.06×0+ 3.35
y= 3.35
the y intercept for this straight line is 57.00
the distance (d) between two points (x1,y1) and (x2,y2) is given by the formula
d = √ ((x2-x1)2+(y2-y1)2)
d = √ (-11-6)2+(4-3)2
d = √ )2+(1)2)
d = √ (289+1)
d = √ 290
the distance between the points is 17.0293863659264
the midpoint of two points is given by the formula
midpoint= ((x1+x2)/2,(y1+y2)/2)
find the x value of the midpoint
xm=(x1+x2)/2
xm=(6+-11)/2=-2.5
find the y value of the midpoint
ym=(y1+y2)/2
ym=(3+4)/2=3.5
the midpoint is: (-2.5,3.5)
graphing the two points, midpoint and distance
p1 (6,3)
p2 (-11,4)
midpoint (-2.5,3.5)
the length of the black line is the distance between the points (17.0293863659264)
find the slope of the line connecting the two points
slope = (y2-y1) = (4-3) = (1) = -0.0588235294117647
(x2-x1) (-11-6) (-17)
find the equation of the line passing through the two points
the general equation for a straight line is
y = mx + b
where m represents the slope of the line which we found in the previous step to be -0.0588235294117647
y = -0.06x + b
we substitute x and y for the values from one of our points (6,3)
3 = -.06×6 + b
3 = -0.35 + b
3--0.35 = b
3.35 = b
knowing both b and m, we can contruct the equation of the line
y= -0.06x+ 3.35
x and y intercepts
the x-intercept is a point on the graph where y is zero
using the equation we found in the previous step and substituting zero for y
y= -0.06x+ 3.35
0= -0.06x+ 3.35
0.06x= 3.35
x= 3.35/0.06 = 57.00
the x intercept for this straight line is 57.00
the y-intercept is a point on the graph where x is zero
using the equation we found in the previous step and substituting zero for x
y= -0.06×0+ 3.35
y= 3.35
the y intercept for this straight line is 57.00 and therefore the awnser is c.
( where 1 ≤ a < 10 and n is an integer )
