Question

1. m = 4; (4, - 5)

a) y + 5 = 4(x - 4)
b) y - 5 = 4(x - 4)
c) y + 5 = 4(x + 4)
d) y - 5 = 4(x + 4)

find an equation of the line having the specified slope and containing the indicated point. write your answer in slope - intercept form.

1. m=-8; (-8, 6)

a) y=-8x - 58
b) y = 8x - 60
c) y=-8x - 66
d) y=-8x - 59

1. m = 8; (0, 6)

a) y = 8x+11
b) y = 8x + 6
c) y = 8x+13
d) y=-8x + 4

multiple choice. choose the one alternative that best completes the statement or answers the question.
find an equation of the line containing the given pair of points. write your final answer in slope - intercept form.

1. (-6, 0) and (5, 3)

a) y=\frac{6}{11}x+\frac{18}{11}
b) y=\frac{3}{11}x+\frac{18}{11}
c) y =-\frac{6}{11}x+\frac{18}{11}
d) y =-\frac{3}{11}x+\frac{18}{11}

short answer. write the word or phrase that best completes each statement or answers the question.
graph the line.

1. y - 2=-\frac{1}{4}(x - 2)

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line.

Step2: Analyze problem 32

Given $m = 4$ and the point $(4,-5)$. Substitute into point - slope form: $y-(-5)=4(x - 4)$, which simplifies to $y + 5=4(x - 4)$. So the answer for 32 is A.

Step3: Analyze problem 33

Given $m=-8$ and the point $(-8,6)$. Using point - slope form $y - 6=-8(x+8)$. Expand: $y-6=-8x - 64$. Then $y=-8x-58$. So the answer for 33 is D.

Step4: Analyze problem 34

Given $m = 8$ and the point $(0,6)$. Using point - slope form $y - 6=8(x - 0)$, which simplifies to $y=8x + 6$. So the answer for 34 is B.

Step5: Analyze problem 36

First find the slope $m$ using the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$ for the points $(-6,0)$ and $(5,3)$. $m=\frac{3-0}{5+6}=\frac{3}{11}$. Then use the point - slope form with the point $(-6,0)$: $y-0=\frac{3}{11}(x + 6)$. Expand to get $y=\frac{3}{11}x+\frac{18}{11}$. So the answer for 36 is B.

Step6: Analyze problem 35

Rewrite the equation $y - 2=-\frac{1}{4}(x - 2)$ in slope - intercept form $y=mx + b$. Expand: $y-2=-\frac{1}{4}x+\frac{1}{2}$. Then $y=-\frac{1}{4}x+\frac{1}{2}+2=-\frac{1}{4}x+\frac{5}{2}$. To graph, the $y$ - intercept is $\frac{5}{2}$ and the slope is $-\frac{1}{4}$. Plot the $y$ - intercept $(0,\frac{5}{2})$ and use the slope to find another point. Move 4 units to the right and 1 unit down to get the point $(4,\frac{3}{2})$. Then draw a line through these two points.

Answer:

1. A. $y + 5=4(x - 4)$
2. D. $y=-8x - 58$
3. B. $y=8x + 6$
4. B. $y=\frac{3}{11}x+\frac{18}{11}$
5. Graph with $y$ - intercept at $(0,\frac{5}{2})$ and slope $-\frac{1}{4}$