Question

name______________________ date: ______ period: __point-slope form (practice worksheet)write an equation in point-slope form of the line that passes through the given point and has the given slope.1. (2, 7); $m = -4$2. (12, 5); $m = -3$3. (4, -5); $m = 6$4. (-6, -2); $m = 3$5. (7, -6); $m = \frac{1}{2}$6. (-8, 2); $m = -\frac{3}{4}$graph the equations below.7. $y + 4 = -3(x + 2)$8. $y + 3 = -2(x - 2)$9. $y - 1 = 3(x + 6)$10. $y + 4 = \frac{-3}{2}(x - 3)$write an equation in point-slope form of the line graphed below. (use the right hand point)11. 12.13.write an equation in point-slope form of the line that passes through the two points given. use the first point to write the equation.14. (4,7) and (5, 1)15. (9, -2) and (-3, 2)16. (3, -8) and 7(-2)

Explanation:

Step1: Recall point-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.

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Section 1: Write point-slope from point & slope

Step2: Solve (2,7); m=-4

Substitute $(x_1,y_1)=(2,7)$, $m=-4$:
$y-7=-4(x-2)$

Step3: Solve (12,5); m=-3

Substitute $(x_1,y_1)=(12,5)$, $m=-3$:
$y-5=-3(x-12)$

Step4: Solve (4,-5); m=6

Substitute $(x_1,y_1)=(4,-5)$, $m=6$:
$y-(-5)=6(x-4)$ or $y+5=6(x-4)$

Step5: Solve (-6,-2); m=3

Substitute $(x_1,y_1)=(-6,-2)$, $m=3$:
$y-(-2)=3(x-(-6))$ or $y+2=3(x+6)$

Step6: Solve (7,-6); m=$\frac{1}{2}$

Substitute $(x_1,y_1)=(7,-6)$, $m=\frac{1}{2}$:
$y-(-6)=\frac{1}{2}(x-7)$ or $y+6=\frac{1}{2}(x-7)$

Step7: Solve (-8,2); m=$-\frac{3}{4}$

Substitute $(x_1,y_1)=(-8,2)$, $m=-\frac{3}{4}$:
$y-2=-\frac{3}{4}(x-(-8))$ or $y-2=-\frac{3}{4}(x+8)$

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Section 2: Graphing (Key Points for Each Line)

Step8: Graph $y+4=-3(x+2)$

Identify point $(-2,-4)$, slope $m=-3$ (down 3, right 1).

Step9: Graph $y+3=-2(x-2)$

Identify point $(2,-3)$, slope $m=-2$ (down 2, right 1).

Step10: Graph $y-1=3(x+6)$

Identify point $(-6,1)$, slope $m=3$ (up 3, right 1).

Step11: Graph $y+4=-\frac{3}{2}(x-3)$

Identify point $(3,-4)$, slope $m=-\frac{3}{2}$ (down 3, right 2).

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Section 3: Write point-slope from graph (use right-hand point)

Step12: Solve Graph 11

Right-hand point: $(4,1)$, slope $m=-\frac{1}{4}$
$y-1=-\frac{1}{4}(x-4)$

Step13: Solve Graph 12

Right-hand point: $(2,4)$, slope $m=3$
$y-4=3(x-2)$

Step14: Solve Graph 13

Right-hand point: $(4,2)$, slope $m=\frac{1}{2}$
$y-2=\frac{1}{2}(x-4)$

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Section 4: Write point-slope from two points (use first point)

Step15: Solve (4,7) & (5,1): Find slope

$m=\frac{1-7}{5-4}=\frac{-6}{1}=-6$
Substitute first point $(4,7)$:
$y-7=-6(x-4)$

Step16: Solve (9,-2) & (-3,2): Find slope

$m=\frac{2-(-2)}{-3-9}=\frac{4}{-12}=-\frac{1}{3}$
Substitute first point $(9,-2)$:
$y-(-2)=-\frac{1}{3}(x-9)$ or $y+2=-\frac{1}{3}(x-9)$

Step17: Solve (3,-8) & (7,-2): Find slope

$m=\frac{-2-(-8)}{7-3}=\frac{6}{4}=\frac{3}{2}$
Substitute first point $(3,-8)$:
$y-(-8)=\frac{3}{2}(x-3)$ or $y+8=\frac{3}{2}(x-3)$

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Answer:

Section 1:

1. $y-7=-4(x-2)$
2. $y-5=-3(x-12)$
3. $y+5=6(x-4)$
4. $y+2=3(x+6)$
5. $y+6=\frac{1}{2}(x-7)$
6. $y-2=-\frac{3}{4}(x+8)$

Section 2 (Graphing Guidelines):

1. For $y+4=-3(x+2)$: Plot $(-2,-4)$, use slope $-3$ to draw the line
2. For $y+3=-2(x-2)$: Plot $(2,-3)$, use slope $-2$ to draw the line
3. For $y-1=3(x+6)$: Plot $(-6,1)$, use slope $3$ to draw the line
4. For $y+4=-\frac{3}{2}(x-3)$: Plot $(3,-4)$, use slope $-\frac{3}{2}$ to draw the line

Section 3:

1. $y-1=-\frac{1}{4}(x-4)$
2. $y-4=3(x-2)$
3. $y-2=\frac{1}{2}(x-4)$

Section 4:

1. $y-7=-6(x-4)$
2. $y+2=-\frac{1}{3}(x-9)$
3. $y+8=\frac{3}{2}(x-3)$