The points (9,1) and (8,6) fall on a particular line. What is its equation in point-slope form?

Answer 1

First, remind yourself that the point-slope equation of a line is: y-y₁ = m(x-x₁)

where (x₁, y₁) is a point on the line and m is the slope.

You already are provided two points from the question itself - (9,1) and (8,6). Either of these can be plugged into the equation for (x₁, y₁).

Now we need to calculate the slope. Recall the formula for slope is m = (y₂-y₁)/(x₂-x₁), where (x₁,y₁) and (x₂,y₂) are two points on the line. You are already given these two points (9,1) and (8,6). Just plug these values into the equation to obtain a value for m. (Hint- to check your answer, I got -5 for the slope).

Now that you have the slope and two points on the line, plug the value of the slope into m and either one of the points for (x₁, y₁), in the point slope form equation: y-y₁ = m(x-x₁).

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Answer 2

(9,1) & (8,6)

y - 1 = [(6 - 1) / (8 - 9)] ( x - 9)

y = ( 5 / -1 ) ( x - 9 ) + 1

y = - 5x + 45 + 1

y = -5x + 46 is the equation of the line in slope intercept form.

Any equation that does not have the y isolated on one side with a coefficient of 1 and x with a slope as the coefficient of x on the right as well as the y intercept on the right is not the slope intercept form.

Answer 3

The point-slope form for the equation of a line is y - y₁ = m(x - x₁) where:

1. (x₁, y₁) is a point that exists on the line (that is not an intercept)
2. m is the slope

The slope can be found using the following formula: (y₂ - y₁) / (x₂ - x₁) where:

1. (x₁, y₁) and (x₂, y₂) are points that exist on the line
2. The slope is (6 - 1) / (8 - 9) = -5

So, we have our slope, m, and a point that exists on the line (let's choose (9, 1)). Putting it all together, the equation of the line is: y - 1 = -5(x - 9)

Hope this was helpful.