Question

The slope and one point on the line are given. Find the equation of the line (in slope-intercept form).(1/4, -3) ; m = -3 y=

Answer 1

Given:

There are given the point and value of slope:

`\begin{gathered} Point:((1)/(4),-4) \\ m=-3 \end{gathered}`

Step-by-step explanation:

To find the equation of the line, we need to use the slope-intercept form of the equation:

So,

From the slope-intercept form:

`y=mx+b`

Where,

`\begin{gathered} x=(1)/(4) \\ y=-4 \\ m=-3 \end{gathered}`

Now,

We need to find the value of b.

So,

To find the value of b, we need to put all the above values into the above formula:

Then,

`\begin{gathered} y=mx+b \\ -4=(-3)(1)/(4)+b \\ -4=-(3)/(4)+b \\ -4+(3)/(4)=-(3)/(4)+b+(3)/(4) \\ b=(3)/(4)-4 \end{gathered}`

Then,

`\begin{gathered} b=(3)/(4)-4 \\ b=(3-16)/(4) \\ b=-(13)/(4) \end{gathered}`

Then,

Put the value of b and m into the formula:

So,