Question

What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1)?

Answer 1

Answer: The answer is (D) $y-1=\dfrac{3}{2}(x+3).$

Step-by-step explanation:  We are given to find the equation of a line which is parallel to the line in the graph and passing through the point (-3, 1).

The points (-2, -4) and (2, 2) lie on the line in the graph, so its slope will be

$m=\dfrac{2+4}{2+2}=\dfrac{6}{4}=\dfrac{3}{2}.$

The slope of the line parallel to the line in the graph will also be same. Since the new line passes through the point (-3, 1), so the equation of the line will be

$y=1=m(x+3)\\\\\Rightarrow y-1=\dfrac{3}{2}(x+3),$

which is in the slope-intercept form.

Thus, the correct option is (D).