Question

hw - 04.01 ready, set, go
possible points: 6.67
match the equation of the line, in point - slope form, with its given points.
k (0,0); l (-4,5)
x (-1,7); y (3,-1)
t (-1,-9); v (5,18)
$y = \frac{9}{2}(x + 1) - 9$ $y = -\frac{5}{4}x$ $y = -2(x + 1) + 7$

Explanation:

Step 1: Recall the point - slope formula and slope formula

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope. The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step 2: Find the slope for $K(0,0)$ and $L(-4,5)$

Using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, with $x_1 = 0,y_1 = 0,x_2=-4,y_2 = 5$.
$m=\frac{5 - 0}{-4-0}=\frac{5}{-4}=-\frac{5}{4}$
The point - slope form using the point $(0,0)$ ($x_1 = 0,y_1 = 0$) is $y-0=-\frac{5}{4}(x - 0)$, which simplifies to $y =-\frac{5}{4}x$.

Step 3: Find the slope for $X(-1,7)$ and $Y(3,-1)$

Using the slope formula with $x_1=-1,y_1 = 7,x_2 = 3,y_2=-1$.
$m=\frac{-1 - 7}{3-(-1)}=\frac{-8}{4}=-2$
The point - slope form using the point $(-1,7)$ ($x_1=-1,y_1 = 7$) is $y - 7=-2(x+1)$, which can be rewritten as $y=-2(x + 1)+7$.

Step 4: Find the slope for $T(-1,-9)$ and $V(5,18)$

Using the slope formula with $x_1=-1,y_1=-9,x_2 = 5,y_2 = 18$.
$m=\frac{18-(-9)}{5-(-1)}=\frac{18 + 9}{6}=\frac{27}{6}=\frac{9}{2}$
The point - slope form using the point $(-1,-9)$ ($x_1=-1,y_1=-9$) is $y+9=\frac{9}{2}(x + 1)$, which can be rewritten as $y=\frac{9}{2}(x + 1)-9$.

Answer:

• $K(0,0);L(-4,5)$ matches with $y =-\frac{5}{4}x$
• $X(-1,7);Y(3,-1)$ matches with $y=-2(x + 1)+7$
• $T(-1,-9);V(5,18)$ matches with $y=\frac{9}{2}(x + 1)-9$