Question

This table gives a few
(
x
,
y
)
(x,y)left parenthesis, x, comma, y, right parenthesis pairs of a line in the coordinate plane.
x
xx
y
yy
−
3
6
−36minus, 36
−
1
1
7
−117minus, 117
−
2
7
−27minus, 27
−
9
8
−98minus, 98
−
1
8
−18minus, 18
−
7
9
−79minus, 79
What is the
y
yy-intercept of the line?
(

Answer 1

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

$m=\frac{y2-y1}{x2-x1}$

take the points

(-27,-98) and (-18,-79)

substitute the values

$m=\frac{-79+98}{-18+27}$

$m=\frac{19}{9}$

step 2

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=\frac{19}{9}$

$point\ (-18,-79)$

substitute

$y+79=\frac{19}{9}(x+18)$ ----> equation in point slope form

step 3

Convert the equation in slope intercept form

$y=mx+b$

where

m is the slope

b is the y-coordinate of the y-intercept

isolate the variable y

$y+79=\frac{19}{9}x+(18)\frac{19}{9}$

$y=\frac{19}{9}x+(18)\frac{19}{9}-79$

$y=\frac{19}{9}x+38-79$

$y=\frac{19}{9}x-41$

therefore

$b=-41$

The y-intercept of the line is the point (0,-41)

Answer 2

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:

$(y-y_1) = \displaystyle\frac{y_2-y_2}{x_2-x_1}(x-x_1)$

where, $(x_1,y_1), (x_2.y_2)$ is the point through which the line passes.

The equation of line passing through (-27,-98) and (-18,-79) is:

$(y+98) = \displaystyle\frac{-79 +98}{-18 + 27}(x-+27)\\\\(y+98)= \frac{19}{9}(x+27)\\\\9(y+98) = 19(x + 27)\\9y = 19x - 369\\\\y = \frac{19}{9}x - 41$

Comparing the above equation with point slope form:

$y = mx + c$

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