Question

homework 10: writing linear equationsdirections: review the following notes box below and complete the problems. be sure to show all the work.*** khan academy video: intro. to point slope form - https://youtu.be/k_oi9la54aa - watch this video for extra support.step 1 find the slope of the line.step 2 use the slope and one of the points to write an equation of the line in point-slope form.another wayyou can use either of the given points to write an equation of the line.use $m = -2$ and $(3, -2)$.$y - (-2) = -2(x - 3)LXB0y = -2x + 4$example 2 using two points to write an equationwrite an equation in slope-intercept form of the line shown.solutionstep 1 find the slope of the line.$m = \frac{-2 - 2}{3 - 1} = \frac{-4}{2}$, or $-2$step 2 use the slope $m = -2$ and the point $(1, 2)$ to write an equation of the line.$y - y_1 = m(x - x_1)$$y - 2 = -2(x - 1)$$y - 2 = -2x + 2$$y = -2x + 4$write the point-slope form.substitute $-2$ for $m$, 1 for $x_1$, and 2 for $y_1$.distributive propertywrite in slope-intercept form.the equation is $y = -2x + 4$.directions: write a linear equation that passes through the given two points.1. $(-4, -2)$ and $(4, 0)$2. $(3, 4)$ and $(0, 5)$3. $(0, 1)$ and $(5, 3)$4. $(2, -2)$ and $(0, -1)$

Explanation:

Problem 1: (-4, -2) and (4, 0)

Step1: Calculate the slope

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{0-(-2)}{4-(-4)}=\frac{2}{8}=\frac{1}{4}$

Step2: Use point-slope form

Use point $(4,0)$: $y-y_1=m(x-x_1)$
$y-0=\frac{1}{4}(x-4)$

Step3: Simplify to slope-intercept

$y=\frac{1}{4}x - 1$

Problem 2: (3, 4) and (0, 5)

Step1: Calculate the slope

$m=\frac{5-4}{0-3}=\frac{1}{-3}=-\frac{1}{3}$

Step2: Use point-slope form

Use point $(0,5)$: $y-5=-\frac{1}{3}(x-0)$

Step3: Simplify to slope-intercept

$y=-\frac{1}{3}x + 5$

Problem 3: (0, 1) and (5, 3)

Step1: Calculate the slope

$m=\frac{3-1}{5-0}=\frac{2}{5}$

Step2: Use point-slope form

Use point $(0,1)$: $y-1=\frac{2}{5}(x-0)$

Step3: Simplify to slope-intercept

$y=\frac{2}{5}x + 1$

Problem 4: (2, -2) and (0, -1)

Step1: Calculate the slope

$m=\frac{-1-(-2)}{0-2}=\frac{1}{-2}=-\frac{1}{2}$

Step2: Use point-slope form

Use point $(0,-1)$: $y-(-1)=-\frac{1}{2}(x-0)$

Step3: Simplify to slope-intercept

$y=-\frac{1}{2}x - 1$

Answer:

1. $y=\frac{1}{4}x - 1$
2. $y=-\frac{1}{3}x + 5$
3. $y=\frac{2}{5}x + 1$
4. $y=-\frac{1}{2}x - 1$