Question

What is the y-intercept of the line that contains the points (3, 3) and (6, 1)?

Answer 1

Answer: Y-intercept = 5

Explanation:

Our task is to find the y-intercept of the line that has the following points:

• (3,3) and (6,1)

Follow these steps:

1. By using the Slope Formula, find the slope.
2. Then, find the line's point-slope equation, using the slope and a point.
3. Convert it to slope-intercept.
4. By looking at the constant term, find the y-intercept.

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STEP ONE

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The slope formula is:

`\sf{m=\cfrac{y_2-y_1}{x_2-x_1}}`

Plug in the parameters:

`\sf{m=\cfrac{1-3}{6-3}=\cfrac{-2}{3}}=-\cfrac{2}{3}}`

`\therefore` Slope = - 2/3

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STEP TWO

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The point-slope formula is:

`\large\boldsymbol{y-y_1=m(x-x_1)}`

In this formula:

• the slope is m;
• the point is (x_1,y_1)

Plug in the parameters:

`\large\boldsymbol{y-3=-\cfrac{2}{3}(x-3)}}`

This is our point-slope equation. We're now moving on to step three.

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STEP THREE

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Use the distributive property:

`\large\boldsymbol{y-3=-\cfrac{2}{3}x+2}`

Add 3 to both sides.

`\boxed{\large\boldsymbol{y=-\cfrac{2}{3}x+5}}`

And, finally, let's find the y-intercept.

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STEP FOUR

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To find the y-intercept, look at the constant term in the equation y = -2/3x + 5.

The constant term is 5; hence, that's the y-intercept.

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THE END

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