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Linear Equations

Linear equations are often organized in slope-intercept form:

[tex]y=mx+b[/tex]

  • m = slope
  • b = y-intercept (the value of y when x=0)

Parallel Lines

Parallel lines always have the same slopes and different y-intercepts.

Solving the Question

We're given:

  • The line [tex]y=5-3x[/tex]
  • We must solve for a parallel line that passes through (0,2)

Firstly, rearrange the given line in slope-intercept form:

[tex]y=-3x+5[/tex]

Remember, parallel lines always have the same slope. Therefore, our parallel line would look like this, with a (currently) unknown y-intercept (b):

[tex]y=-3x+b[/tex]

We're given that the line passes through the point (0,2). Because the y-intercept occurs when x=0, we now know that the y-intercept of the line is 2. Plug this into the equation:

[tex]y=-3x+2[/tex]

Answer

[tex]y=-3x+2[/tex]

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