Question

6.3 ws: slope - intercept form given two points
date ______ period
write the slope - intercept form of the equation of the line with the given information. be sure to show all work!

1. through: (1, 5) and (-1, -3)
2. through: (-3, 0) and (-2, -1)
3. through: (-5, -5) and (5, -1)
4. through: (-5, 1) and (-4, -2)
5. through: (-5, -5) and (-2, 4)
6. through: (-2, -4) and (-1, -2)

Explanation:

Problem 1: through (1, 5) and (-1, -3)

Step 1: Calculate the slope ($m$)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1, y_1) = (1, 5)$ and $(x_2, y_2) = (-1, -3)$.
So, $m = \frac{-3 - 5}{-1 - 1} = \frac{-8}{-2} = 4$.

Step 2: Use point - slope form to find the equation

Point - slope form is $y - y_1 = m(x - x_1)$. Using the point $(1, 5)$ and $m = 4$:
$y - 5 = 4(x - 1)$

Step 3: Convert to slope - intercept form ($y = mx + b$)

Expand the right - hand side: $y - 5 = 4x - 4$
Add 5 to both sides: $y = 4x + 1$

Step 1: Calculate the slope ($m$)

Using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, with $(x_1,y_1)=(-3,0)$ and $(x_2,y_2)=(-2,-1)$
$m=\frac{-1 - 0}{-2-(-3)}=\frac{-1}{1}=-1$

Step 2: Use point - slope form

Using the point $(-3,0)$ and $m = - 1$ in $y - y_1=m(x - x_1)$:
$y - 0=-1(x + 3)$

Step 3: Convert to slope - intercept form

Simplify the equation: $y=-x - 3$

Step 1: Calculate the slope ($m$)

Using the slope formula $m = \frac{y_2-y_1}{x_2 - x_1}$, with $(x_1,y_1)=(-5,-5)$ and $(x_2,y_2)=(5,-1)$
$m=\frac{-1-(-5)}{5-(-5)}=\frac{-1 + 5}{10}=\frac{4}{10}=\frac{2}{5}$

Step 2: Use point - slope form

Using the point $(-5,-5)$ and $m=\frac{2}{5}$ in $y - y_1=m(x - x_1)$:
$y+5=\frac{2}{5}(x + 5)$

Step 3: Convert to slope - intercept form

Expand the right - hand side: $y+5=\frac{2}{5}x+2$
Subtract 5 from both sides: $y=\frac{2}{5}x-3$

Answer:

$y = 4x + 1$

Problem 2: through (-3, 0) and (-2, -1)