Question

What is the equation of the line shown in the graph? Drag and drop the expressions to write the equation of the line in slope-intercept form. y = 2x 4x -2x - 4x -2 4 4.07 Unit Test: Li 2​

Answer 1

Answer:y=2x+4

Step-by-step explanation:

Take the points (-3,-2) and (-1,2) and find the slope

the slope formula is y^2-y^1/x^2-x^1
2--2/-1--3

2 subtraction signs next to each other make a positive sign

2+2/-1+3=4/2=2

y=2x+b

Take one of the points and plug it in, I'll use (-1,2)

2=2(-1)+b

2=-2+b

Add 2 on each side to get b alone

2+2=-2+2+b

4=b

Answer 2

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture above

`(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{-1}-\underset{x_1}{(-3)}}} \implies \cfrac{2 +2}{-1 +3} \implies \cfrac{ 4 }{ 2 } \implies 2`

`\begin{array} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-3)}) \implies y +2 = 2 ( x +3) \\\\\\ y+2=2x+6\implies {\Large \begin{array}{llll} y=2x+4 \end{array}}`