Question

review 3
winter term
name___________________ per___
write an equation of the line in slope intercept form ( y = mx + b ).
1.
2.

1. ( y = \frac{2}{-3}x + 5 )
2. ( y = \frac{2}{-3}x + 5 )
3. write an equation in point slope form ( y - y_1 = m(x - x_1) ) of

the line that passes through the point ( (7, -3) ) and has a slope of ( -8 ).

1. ( y + 3 = -8(x - 7) )
2. simplify your answer from #3 into slope intercept form ( y = mx + b )
3. ( y = -8x + 53 )
4. write an equation in point slope form ( y - y_1 = m(x - x_1) ) with the given values:

( f(0) = -2 ), ( f(1) = 2 )

1. ( y - 2 = 4(x - 1) )

Explanation:

Step1: Identify the point and slope

We know that for a function \( f(x) \), when \( x = 0 \), \( f(0)=-2 \), so the point is \( (x_1,y_1)=(0, - 2) \); when \( x = 1 \), \( f(1) = 2 \), so another point is \( (x_2,y_2)=(1,2) \). The slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{2-(-2)}{1 - 0}=\frac{4}{1}=4 \). We can use either point, let's use \( (x_1,y_1)=(0,-2) \) or \( (1,2) \). Let's use \( (1,2) \) as \( (x_1,y_1) \), then \( x_1 = 1,y_1=2 \) and \( m = 4 \).

Step2: Apply point - slope formula

The point - slope form is \( y - y_1=m(x - x_1) \). Substitute \( x_1 = 1 \), \( y_1=2 \) and \( m = 4 \) into the formula, we get \( y - 2=4(x - 1) \). If we use the point \( (0,-2) \), with \( x_1 = 0,y_1=-2 \) and \( m = 4 \), the formula gives \( y-(-2)=4(x - 0) \), that is \( y + 2=4x \), but the more appropriate one using the two given points' relation is \( y - 2=4(x - 1) \) (since we can also calculate slope from \( f(0) \) and \( f(1) \) and use \( (1,2) \) as the point).

Answer:

\( y - 2 = 4(x - 1) \) (or \( y+2 = 4x \) is also correct, but \( y - 2=4(x - 1) \) is more in line with using the point \( (1,2) \))