Question

The point-slope form of the equation of the line that passes through (-5,-1) and (10,-7) 157Wt is the ), What is the standard form of the equation for this line?

Answer 1

`y + 1 = -(2)/(5)(x+5)`

and

2x + 15y = -15

Explanation:

To write the point slope form, a point and a slope is required. Find the slope using the two points given and the slope formula.

`m = (y_2-y_1)/(x_2-x_1)= (-1 --7)/(-5-10)= (6)/(-15) = -(2)/(5)`

Substitute -2/5 and the point (-5,-1) into the form. Then convert to make the standard form of the equation.

`y - y_1 = m(x-x_1)\\y --1=-(2)/(5)(x--5)\\y + 1 = -(2)/(5)(x+5)`

Now convert to standard form by applying the distributive property and moving terms.

`y + 1 = -(2)/(5)(x+5)\\y + 1 = -(2)/(5)x - 2\\y + 3 = -(2)/(5)x\\(2)/(5)x + y +3=0\\2x + 5y + 15 = 0\\2x + 15y = -15`