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:

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

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,

$\begin{gathered} x=\frac{1}{4} \\ y=-4 \\ m=-3 \end{gathered}$

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,

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

Then,

$\begin{gathered} b=\frac{3}{4}-4 \\ b=\frac{3-16}{4} \\ b=-\frac{13}{4} \end{gathered}$

Then,

Put the value of b and m into the formula:

So,