9.5.4. Equation of the Straight Line Given Its Slope and Its y–Intercept

In the form of , find the equation of the straight line that intersects the positive part of the -axis at a point that is 1 unit length away from the origin, given that the straight line is parallel to another line whose equation is .

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Example

In the form of , find the equation of the straight line that intersects the positive part of the -axis at a point that is 1 unit length away from the origin, given that the straight line is parallel to another line whose equation is .

Solution

For straight line graphs, where is the slope and is the -intercept.

The -intercept, , is the point where the line intersects the -axis which we know is 1 from the question.

So we can say,

Our line must be parallel to the line with equation

The equation can be rearranged to get

The slope, , of this line is . So, for our line to be parallel to this one, it must also have a slope of .

Thus, the equation is .

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