Question

Write an equation of the line passing through the given point (2,-5) and having the given

slope m= -6. Write the final answer in slope-intercept form.

Answer 1

The answer is:

y = -6x + 7

Work/explanation:

First, I will write the equation in point slope

`\mapsto\phantom{333}\bf{y-y_1=m(x-x_1)}`

WHERE:

m = slope

(x₁,y₁) is a point

________

Plug in the data:

`\boxed{\large\begin{gathered}\bf{y-(-5)=-6(x-2)}\\\bf{y+5=-6x+12}\\\bf{y=-6x+12-5}\\\bf{y=-6x+7}\end{gathered}}`

Hence, the equation is y = -6x + 7.

Answer 2

y = -6x + 7

Explanation:

To write an equation of the line passing through the point (2,-5) with a slope of m = -6, we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

Where (x1, y1) is the given point and m is the slope.

Substituting the given values, we get:

y - (-5) = -6(x - 2)

Simplifying:

y + 5 = -6x + 12

y = -6x + 7

y = -6x + 7

Therefore, the equation of the line passing through the point (2,-5) with a slope of m = -6 is:

y = -6x + 7