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]
