Write the slope-intercept form of the equation that passes through the point (3,-2) and is parallel to the line y = -x - 5

The equation of the line is y = -x + 1

Step-by-step explanation:

* Lets explain how to solve the problem

- The slope-intercept form of the equation is y = mx + c, where m is

 the slope of the line and c is the y-intercept

- To make this equation you need slope (m) and a point on the line to

 find the value of c

- The parallel lines have same slopes

* Lets solve the problem

- The line is parallel to the line y = -x - 5

∵ y = mx + c

∵ The slope of the line y = -x - 5 is the coefficient of x

∴ m = -1

∵ Parallel lines have same slopes

∴ The slope of the line is -1

∴ the equation of the line is y = -x + c

- To find c substitute x and y in the equation by the coordinates of

  any point lies on the line

∵ The line passes through point (3 , -2)

∵ y = -x + c

∴ -2 = -(3) + c

∴ -2 = -3 + c ⇒ add 3 for both sides

∴ c = 1

∴ The equation of the line is y = -x + 1

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