Question

Type an equation for the line described. Type your answer in the form g(x)=mx+b. If a value is not an integer type it as a decimal rounded to the nearest hundredth. Do not put any spaces between your characters.A line parallel to f(x)=-5x-3 and passing through the point (2,12) The slope of our parallel line will be Answer and it has an equation of g(x)=Answer.

Answer 1

A line equation written in slope-intercept form is

$y=mx+b$

Where m represents the slope of the line and b the y-intercept. The given line in the text is

$f(x)=-5x-3$

This line have a slope equal to - 5 and an intercept equal to - 3. Parallel lines have the same slope, therefore, our desired line have the following format

$g(x)=-5x+b$

To find the intercept, we can use the point that belongs to our line.

$g(2)=12\Rightarrow12=-5\cdot2+b\Rightarrow b=22$

Then, our line is

$g(x)=-5x+22$