Question

Find the equation of this line.

Simplify the fractions

Answer 1

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

Explanation:

Hi there!

Linear equations are typically organized in slope-intercept form:
`y=mx+b` where m is the slope and b is the y-intercept (the value of y when x=0).

First, we must find the slope (m).

`m=\displaystyle(y_2-y_1)/(x_2-x_1)` where two points that fall on the line are
`(x_1,y_1)` and
`(x_2,y_2)`

Two points that are highlighted for us on the graph are (-3,-2) and (5,4). Plug these into the equation:

`m=\displaystyle(4-(-2))/(5-(-3))\\\\m=\displaystyle(4+2)/(5+3)\\\\m=\displaystyle(6)/(8)\\\\m=(3)/(4)`

Therefore, the slope of the line is 3/4. Plug this into
`y=mx+b`:

`y=\displaystyle(3)/(4) x+b`

Now, to find the y-intercept (b), our first resort would be to find it on the graph. However, on the graph, it appears ambiguous. So, we must solve it algebraically.

`y=\displaystyle(3)/(4) x+b`

Plug in the point (5,4) and solve for b:

`4=\displaystyle(3)/(4) (5)+b\\\\4=\displaystyle(15)/(4)+b\\\\b=4-(15)/(4) \\\\b=(1)/(4)`

Therefore, the y-intercept is
`\displaystyle (1)/(4)`. Plug this back into
`y=\displaystyle(3)/(4) x+b`:

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

I hope this helps!