Question

Write the equation of the line that is parallel to the line 3x − y = −3 and passes through the point (4, −2).

Answer 1

first change the given equation to slope-intercept form \[\implies y = 3x + 3\]
the slope here is 3 so the parallel line would have a slope of 3 also

now use point-slope form \[y - y_1 = m(x-x_1)\]
\[\implies y - (-2) = 3(x-4)\]
simplify
\[\implies y + 2 = 3x - 12\]
subtract 2 from both sides
\[\implies y = 3x - 14\]