A line passes through the point , 6−1 and has a slope of −43. Write an equation in point-slope form for this line.

Answer 1

y - y₁ = m(x - x₁)

x₁ = 6

y₁ = -1

m = -43

y + 1 = -43(x - 6)

Answer 2

Thank you for your question.

The point-slope formula is: y-y₁=m(x-x₁).

In this formula, the m= the slope and the y_{1 and} x₁ represent the coordinates of a point.

Since the question gives a slope of -43, you will plug this in for m.

You will then plug the x-coordinate given (6) and the y-coordinate given (-1) in for the x₁ and y₁ in the equation.

Plugging these figures into the y-y₁=m(x-x₁) equation gives you-->

y- (-1)=-43(x-6)

**If the teacher wants you to leave the equation in the point-slope form without simplifying, you could leave it that way.

However, you can also simplify the equation further, all the way to the slope-intercept form of y=mx+b.

(You just might not want to do this in cases where you need to leave it as the point-slope form. However, I will show it down below for a future reference for times when there is a question that wants you to do that...)

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You then multiply what's inside the parentheses on the right hand side of the equation by the slope, and take the double negative signs on the left hand side of the equation and make it a plus (**remember that multiplying a negative by a negative (-43 * -6) will give a positive product)-->

y+1=-43(x) + -43 (-6)

y+1=-43x+258

You could then combine like terms and simplify the equation into the slope-intercept form ( y=mx+b) by doing so-->

y+1=-43x+258

-1 -1

y=-43x+257

I hope this helps!

Have a great night!

Answer 3

Given point P(x₁,y₁) and slope m, the point-slope formula for the equation of the line is:

(y - y₁) = m(x - x₁)

For this problem:

(y - (-1)) = -43(x - 6)

Note: If you change this formula, you may be getting slope-intercept or some other form.

Answer 4

Start with point-slope form:(y - y₁) = m(x - x₁)

(y - 6) = -43(x + 1)