Respuesta :
Answer:
The y-intercept of the line is the point (0,-41)
Step-by-step explanation:
we have the points
(-36,-117),(-27,-98) and (-18,-79)
step 1
Find the slope of the linear equation
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
take the points
(-27,-98) and (-18,-79)
substitute the values
[tex]m=\frac{-79+98}{-18+27}[/tex]
[tex]m=\frac{19}{9}[/tex]
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{19}{9}[/tex]
[tex]point\ (-18,-79)[/tex]
substitute
[tex]y+79=\frac{19}{9}(x+18)[/tex] ----> equation in point slope form
step 3
Convert the equation in slope intercept form
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-coordinate of the y-intercept
isolate the variable y
[tex]y+79=\frac{19}{9}x+(18)\frac{19}{9}[/tex]
[tex]y=\frac{19}{9}x+(18)\frac{19}{9}-79[/tex]
[tex]y=\frac{19}{9}x+38-79[/tex]
[tex]y=\frac{19}{9}x-41[/tex]
therefore
[tex]b=-41[/tex]
The y-intercept of the line is the point (0,-41)
Answer:
y-intercept of line is -41
Step-by-step explanation:
We are given the following in the question:
The line passes through the given coordinates point:
(-36,-117),(-27,-98) and (-18,-79)
The equation of line can be made with the help of two point form of straight line.
The equation of line is given by:
[tex](y-y_1) = \displaystyle\frac{y_2-y_2}{x_2-x_1}(x-x_1)[/tex]
where, [tex](x_1,y_1), (x_2.y_2)[/tex] is the point through which the line passes.
The equation of line passing through (-27,-98) and (-18,-79) is:
[tex](y+98) = \displaystyle\frac{-79 +98}{-18 + 27}(x-+27)\\\\(y+98)= \frac{19}{9}(x+27)\\\\9(y+98) = 19(x + 27)\\9y = 19x - 369\\\\y = \frac{19}{9}x - 41[/tex]
Comparing the above equation with point slope form:
[tex]y = mx + c[/tex]
where m is the slope of the line and c is the y-intercept, we get c = - 41
Thus, y-intercept of line is -41
