Question

Find the equation of a line with given slope and containing the given point. Write the equation in slope-intercept form. M= -2, point ( 2,1 )Y=

Answer 1

y = -2x + 5

Explanation:

Pre-Solving

We are given that a line contains the point (2,1) and a slope (m) of -2.

We want to write the equation of this line in slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y-intercept.

Solving

Since we are already given the slope of the line, we can plug that value into the equation.

Replace m with -2.

y = -2x + b

Now, we need to solve for b.

As the line passes through (2,1), we can use those values to help solve for b.

Substitute 2 as x and 1 as y.

1 = -2(2) + b

Multiply.

1 = -4 + b

Add 4 to both sides.

5 = b

Substitute 5 as b.

y = -2x + 5

Answer 2

The equation of a line in slope-intercept form is;

`y=mx+b`

For the given information, that is the slope and a point on the line, we now have;

`\begin{gathered} (x,y)=(2,1) \\ m=-2 \\ y=mx+b\text{ now becomes;} \\ 1=-2(2)+b \\ 1=-4+b \\ \text{Add 4 to both sides} \\ 1+4=-4+4+b \\ 5=b \\ \text{Now that we have }\det er\min ed\text{ the value of b,} \\ We\text{ can substitute for m and b as follows; } \\ y=mx+b\text{ becomes;} \\ y=-2x+5 \end{gathered}`

ANSWER:

The equation of the line therefore is;

`y=-2x+5`