Slope Intercept
If a straight line passes through point (6, 2) and is parallel to y=3x-1, what is its equation?
Expand Hint
The standard form of an equation, which is also known as slope-intercept form:
$$$y=mx+b$$$
where
$$m$$
is the slope and
$$b$$
is the line’s intersection along the y-axis.
Hint 2
Slopes of perpendicular lines are the negative reciprocals of each other. Parallel lines have identical slopes.
The standard form of an equation, which is also known as slope-intercept form:
$$$y=mx+b$$$
where
$$m$$
is the slope and
$$b$$
is the line’s intersection along the y-axis.
In the given parallel line,
$$y=3x-1$$
, the slope is 3. Slopes of parallel lines have identical slopes, meaning the unknown straight line has a slope of 3. The starting equation:
$$$y=3x+b$$$
Because the unknown equation passes through the point (6, 2), let’s substitute those coordinates:
$$$2=3(6)+b$$$
Solving for
$$b$$
:
$$$b=2-18=-16$$$
Because the point where the straight line passes through the y-axis is now known, the final equation is:
$$$y=3x-16$$$
$$$y=3x-16$$$
Time Analysis
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