Question

Write the equation in slope-intercept form. Then find the slope and y-intercept of the line.5x+6y=3

Answer 1

• The slope of the line = -5/6

,

• The y-intercept of the line = 1/2

Explanation:

Given the equation of the line below:

`5x+6y=3`

We are required to:

• Write the equation in ,slope-intercept form,.

,

• Find the slope and y-intercept of the line.

The slope-intercept form of the equation of a straight line is:

`\begin{equation} y=mx+b\text{ where }\begin{cases}m={slope} \\ b={y-intercept}\end{cases} \end{equation}`

So, first, make y the subject of the given equation:

`\begin{gathered} 5x+6y=3 \\ \text{Subtract 5x from both sides of the equation} \\ 5x-5x+6y=-5x+3 \\ 6y=-5x+3 \\ \text{Divide all through by 6} \\ (6y)/(6)=-(5)/(6)x+(3)/(6) \\ y=-(5)/(6)x+(3)/(6) \\ y=-(5)/(6)x+(1)/(2) \end{gathered}`

Next, compare with the form given above:

`\begin{gathered} Slope,m=-(5)/(6) \\ y-intercept,b=(1)/(2) \end{gathered}`

• The slope of the line = -5/6

,

• The y-intercept of the line = 1/2