Question

Find the equation of this line (No need to show work, be fast please.)

Answer 1

We are given the graph of a line and asked to find its equation. Recall that we can write the equation of a line as

`y\text{ - y\_0=m\lparen x - x\_0\rparen}`

where (x0, y0) is point on the line and m is the slope of the line.

From the graph, we can identify that points (-3, -2) and (5,4) are on the line. Now let us calculate the slope of the line.

Recall that given points (a,b) and (c,d), the slope of the line that passes through them is given by the formula

`m=\frac{d\text{ -b}}{c\text{ -a}}=\frac{b\text{ -d}}{a\text{ - c}}`

In our case we got a=-3, b=-2, c=5 and d=4. So we have

`m\text{ = }\frac{4\text{ - \lparen-2\rparen}}{5\text{ - \lparen-3\rparen}}=(4+2)/(5+3)=(6)/(8)=(3)/(4)`

Now, we can use the fact that the point (5,4) is on the line. So we use it as our (x0,y0). So our equation would be

`y\text{ - 4=}(3)/(4)(x\text{ - 5\rparen}`

which is equivalent to

`y\text{ - 4=}(3)/(4)x\text{ - }(15)/(4)`

Now, we add 4 on both sides, so we get

`\begin{gathered} y=(3)/(4)x\text{ -}(15)/(4)+4=(3)/(4)x\text{ -}(15)/(4)+(16)/(4) \\ =(3)/(4)x+(1)/(4) \end{gathered}`

so the equation of the line is

`y=(3)/(4)x+(1)/(4)`