Question

bell: 3rdhomework 6: writing linear equations(given point & slope)directions: given the point and slope, write the equation of the line.1. (4, 2); slope = 32. (0, 3); slope = -23. (1, -7); slope = -14. (-5, -3); slope = $-\frac{3}{5}$5. (-8, 6); slope = $\frac{1}{4}$6. (9, -4); slope = $-\frac{2}{3}$7. (6, -6); slope = $\frac{5}{6}$8. (-8, 9); slope = $-\frac{3}{2}$9. (-2, -11); slope = 410. (-4, 0); slope = $\frac{1}{2}$

Explanation:

We use the point-slope form of a line: $y - y_1 = m(x - x_1)$, where $(x_1,y_1)$ is the given point and $m$ is the slope. We will rearrange to slope-intercept form $y=mx+b$ for each problem.

1. Step1: Substitute values into point-slope

$y - 2 = 3(x - 4)$

Step2: Simplify to slope-intercept

$y - 2 = 3x - 12$
$y = 3x - 10$

2. Step1: Substitute values into point-slope

$y - 3 = -2(x - 0)$

Step2: Simplify to slope-intercept

$y = -2x + 3$

3. Step1: Substitute values into point-slope

$y - (-7) = -1(x - 1)$

Step2: Simplify to slope-intercept

$y + 7 = -x + 1$
$y = -x - 6$

4. Step1: Substitute values into point-slope

$y - (-3) = -\frac{3}{5}(x - (-5))$

Step2: Simplify to slope-intercept

$y + 3 = -\frac{3}{5}(x + 5)$
$y + 3 = -\frac{3}{5}x - 3$
$y = -\frac{3}{5}x - 6$

5. Step1: Substitute values into point-slope

$y - 6 = \frac{1}{4}(x - (-8))$

Step2: Simplify to slope-intercept

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

6. Step1: Substitute values into point-slope

$y - (-4) = -\frac{2}{3}(x - 9)$

Step2: Simplify to slope-intercept

$y + 4 = -\frac{2}{3}x + 6$
$y = -\frac{2}{3}x + 2$

7. Step1: Substitute values into point-slope

$y - (-6) = \frac{5}{6}(x - 6)$

Step2: Simplify to slope-intercept

$y + 6 = \frac{5}{6}x - 5$
$y = \frac{5}{6}x - 11$

8. Step1: Substitute values into point-slope

$y - 9 = -\frac{3}{2}(x - (-8))$

Step2: Simplify to slope-intercept

$y - 9 = -\frac{3}{2}(x + 8)$
$y - 9 = -\frac{3}{2}x - 12$
$y = -\frac{3}{2}x - 3$

9. Step1: Substitute values into point-slope

$y - (-11) = 4(x - (-2))$

Step2: Simplify to slope-intercept

$y + 11 = 4(x + 2)$
$y + 11 = 4x + 8$
$y = 4x - 3$

10. Step1: Substitute values into point-slope

$y - 0 = \frac{1}{2}(x - (-4))$

Step2: Simplify to slope-intercept

$y = \frac{1}{2}(x + 4)$
$y = \frac{1}{2}x + 2$

Answer:

1. $y = 3x - 10$
2. $y = -2x + 3$
3. $y = -x - 6$
4. $y = -\frac{3}{5}x - 6$
5. $y = \frac{1}{4}x + 8$
6. $y = -\frac{2}{3}x + 2$
7. $y = \frac{5}{6}x - 11$
8. $y = -\frac{3}{2}x - 3$
9. $y = 4x - 3$
10. $y = \frac{1}{2}x + 2$