Question

What is an equation of the line that is parallel to y = 5- 3x and passes through (0, 2)?

Answer 1

Linear Equations

Linear equations are often organized in slope-intercept form:

$y=mx+b$

• 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 $y=5-3x$
• We must solve for a parallel line that passes through (0,2)

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

$y=-3x+5$

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

$y=-3x+b$

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:

$y=-3x+2$

Answer

$y=-3x+2$