find the equation of the line. using exact numbers

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

[tex]\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|ll} \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[/tex]

gmany gmany · Answer 2 · 2019-08-10T22:27:12+02:00

Answer:

[tex]\large\boxed{y=\dfrac{3}{4}x-2}[/tex]

Step-by-step explanation:

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

[tex]y=mx+b[/tex]

m - slope

b - y-intercept → (0, b)

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

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

(-4, -5)

(0, -2) → b = -2

Calculate the slope:

[tex]m=\dfrac{-2-(-5)}{0-(-4)}=\dfrac{-2+5}{0+4}=\dfrac{3}{4}[/tex]

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

[tex]y=\dfrac{3}{4}x-2[/tex]