Question

1. what is the slope and y - intercept of the following lines? i) ii) slope = uphill y - int (as ordered pairs)= 0 / - 4 3 / 0 4 / 6 slope = y - int (as ordered pairs)=

Explanation:

Step1: Recall slope - formula

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. The y - intercept is the point where the line crosses the y - axis (i.e., $x = 0$).

Step2: For the first line

Pick two points, say $(-5,0)$ and $(0,4)$. Then $m=\frac{4 - 0}{0-(-5)}=\frac{4}{5}$. The y - intercept is the point $(0,4)$.

Step3: For the second line

Pick two points, say $(-5,4)$ and $(5,2)$. Then $m=\frac{2 - 4}{5-(-5)}=\frac{-2}{10}=-\frac{1}{5}$. The y - intercept is the point where $x = 0$. Using the two - point form $y - y_1=m(x - x_1)$ with $(x_1,y_1)=(-5,4)$ and $m =-\frac{1}{5}$, we have $y-4=-\frac{1}{5}(x + 5)$. When $x = 0$, $y-4=-\frac{1}{5}(0 + 5)=-1$, so $y=3$. The y - intercept is $(0,3)$.

Answer:

i) Slope $=\frac{4}{5}$, y - int (as ordered pair)$=(0,4)$
ii) Slope $=-\frac{1}{5}$, y - int (as ordered pair)$=(0,3)$