Question

Find the equation of the line. using exact numbers

Answer 1

`\large\boxed{y=(3)/(4)x-2}`

Explanation:

The slope-intercept form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept → (0, b)

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

From the graph (look at the picture) we have two points

(-4, -5)

(0, -2) → b = -2

Calculate the slope:

`m=(-2-(-5))/(0-(-4))=(-2+5)/(0+4)=(3)/(4)`

Put it and the value of an y-intercept to the equation of a line:

`y=(3)/(4)x-2`

Answer 2

let's take a peek at the line, to get the equation of a line all we need is two points on it, hmmm let's see say this line passes through (0, -2) and (4, 1), so let's use those

`\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-2)}{4-0}\implies \cfrac{1+2}{4}\implies \cfrac{3}{4} \\\\\\ \begin{array}c \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-2)=\cfrac{3}{4}(x-0) \\\\\\ y+2=\cfrac{3}{4}x\implies y=\cfrac{3}{4}x-2`