Question

this table gives a few (x, y) pairs of a line in the coordinate plane. x y -36 -117 -27 -98 -18 -79 what is the y - intercept of the line? related content intercepts from a table

Explanation:

Step1: Find the slope formula

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-36,-117)$ and $(x_2,y_2)=(-27,-98)$. Then $m=\frac{-98-(-117)}{-27 - (-36)}=\frac{-98 + 117}{-27+36}=\frac{19}{9}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(-36,-117)$ and $m = \frac{19}{9}$, we have $y+117=\frac{19}{9}(x + 36)$.

Step3: Convert to slope - intercept form

Expand the right - hand side: $y+117=\frac{19}{9}x+76$. Then subtract 117 from both sides to get $y=\frac{19}{9}x+76 - 117=\frac{19}{9}x - 41$.

Step4: Identify the y - intercept

In the slope - intercept form $y = mx + b$ (where $b$ is the y - intercept), when $x = 0$, $y=-41$. So the y - intercept is the point $(0,-41)$.

Answer:

$(0,-41)$