Question

lesson 5.3
practice
for use with pages 308-314
write an equation in point-slope form of the line that passes through the given point and has the given slope $m$.

1. $(1,9); m = -3$
2. $(4,-10); m = 2$
3. $(-5,6); m = 4$
4. $(-2,-8); m = 3$
5. $(-4,-7); m = -\frac{1}{2}$
6. $(-9,2); m = -5$
7. $(6,-4); m = \frac{2}{3}$
8. $(0,15); m = \frac{4}{5}$
9. $(-8,0); m = 2$

Explanation:

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

Step1: Substitute for problem 1

Substitute $(x_1,y_1)=(1,9), m=-3$
$y - 9 = -3(x - 1)$

Step2: Substitute for problem 2

Substitute $(x_1,y_1)=(4,-10), m=2$
$y - (-10) = 2(x - 4)$
Simplify sign: $y + 10 = 2(x - 4)$

Step3: Substitute for problem 3

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

Step4: Substitute for problem 4

Substitute $(x_1,y_1)=(-2,-8), m=3$
$y - (-8) = 3(x - (-2))$
Simplify signs: $y + 8 = 3(x + 2)$

Step5: Substitute for problem 5

Substitute $(x_1,y_1)=(-4,-7), m=-\frac{1}{2}$
$y - (-7) = -\frac{1}{2}(x - (-4))$
Simplify signs: $y + 7 = -\frac{1}{2}(x + 4)$

Step6: Substitute for problem 6

Substitute $(x_1,y_1)=(-9,2), m=-5$
$y - 2 = -5(x - (-9))$
Simplify sign: $y - 2 = -5(x + 9)$

Step7: Substitute for problem 7

Substitute $(x_1,y_1)=(6,-4), m=\frac{2}{3}$
$y - (-4) = \frac{2}{3}(x - 6)$
Simplify sign: $y + 4 = \frac{2}{3}(x - 6)$

Step8: Substitute for problem 8

Substitute $(x_1,y_1)=(0,15), m=\frac{4}{5}$
$y - 15 = \frac{4}{5}(x - 0)$
Simplify: $y - 15 = \frac{4}{5}x$

Step9: Substitute for problem 9

Substitute $(x_1,y_1)=(-8,0), m=2$
$y - 0 = 2(x - (-8))$
Simplify: $y = 2(x + 8)$

Answer:

1. $y - 9 = -3(x - 1)$
2. $y + 10 = 2(x - 4)$
3. $y - 6 = 4(x + 5)$
4. $y + 8 = 3(x + 2)$
5. $y + 7 = -\frac{1}{2}(x + 4)$
6. $y - 2 = -5(x + 9)$
7. $y + 4 = \frac{2}{3}(x - 6)$
8. $y - 15 = \frac{4}{5}x$
9. $y = 2(x + 8)$