Determine Equation of Line Practice

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Question 1

Given the points (3,-3) and (-3, 1). Determine the equation of the line that passes through these points.

You can use the picture shown on the right as reference.

slope-intercept form of a line


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Select and check your answer...

A. y= 2x/3 +1
B. y = -2x/3 +1
C. y = -2x/3 -1
D. y = -2x/3 -1

Step by Step Solution

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    Step 1

    First, to determine the equation of the line, we should start with the Slope-Intercept Form of an equation of a line.

    From the picture, we only need to find the values of the slope(m) and y-intercept(b).

    After finding them, we just replace m and b with these values. That's it.

    slope-intercept form of a line
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    Step 2

    Now, with the given 2 points (3,-3) and (-3,1), we can use them to find m using the Slope Formula as shown on the right.

    To use this formula, we need label these points as Point 1 and Point 2. Let's label (3,-3) as Point 1 and (-3,1) as Point 2.

    By doing this, we have:

    x-coordinate and y-coordinate of a point (3.0,-3.0) x-coordinate and y-coordinate of a point (-3.0,1.0)
    slope formula
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    Step 3

    Now, we substitute these values into the slope formula.

    Finding the slope using the Slope Formula

    Hence, the we get the slope, m = -2/3

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    Step 4

    With m = -2/3, the equation becomes:

    Find the y-intercept in y=-2x/3 + b

    Next, we have to find b. To do so, we can pick a point on the line and substitute its x- and y-coordinates into the equation above.

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    Step 5

    We can just pick any of the given points, (3,-3) or (-3, 1). Let's pick the point (-3, 1) where:

    x = -3 and y = 1

    Substituting x and y into the equation, we get:

    Substitute x = -3 and y =1 into y=-2x/3 + b

    Now, let's solve for b:

    Finding the y-intercept

    With this, we have the y-intercept, b as -1

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    Step 6

    With b = -1, the equation becomes:

    Equation of a line with slope and y-intercept found

    From the equation of the line above, clearly the answer is C.