# How do you write an equation of a line with point (2,5), slope -2?

May 19, 2018

y−5=-2(x−2)

and

$y = - 2 x + 9$

are correct.

#### Explanation:

Point slope form of a line is the standard equation:

y−y_1=m(x−x_1)

where ${x}_{1}$ and ${y}_{1}$ are a point the line intersects and $m$ in the slope, so your line:

y−5=-2(x−2) is your line.

you can convert it to slope intercept form:

$y = - 2 x + 9$

so the slope $m = - 2$ and the y-intercept is 9

graph{y=-2x +9 [-17.04, 22.96, -5.36, 14.64]}

May 19, 2018

$y = - 2 x + 9$

#### Explanation:

We must assume that the line is a straight line.

The equation of a straight line in slope/point form is:

$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$

Where the line has a slope $m$ and passes through the point $\left({x}_{1} , {y}_{1}\right)$

Here we have a line of slope $- 2$ passing through the point $\left(2 , 5\right)$

$\therefore \left(y - 5\right) = - 2 \left(x - 2\right)$

$y = - 2 x + 4 + 5$

$y = - 2 x + 9$
is the equation of the line in slope/intercept form.