Question

If a is a non-zero constant, what is the equation for a line parallel to the line y = ax + 6 and passing through the point (3, -5)?

Answer 1

Answer:

y=ax-(3a+5).

Explanation:

Given the line:

$y=ax+6$

Comparing with the slope-intercept form: y=mx+b

• The slope of the line, m = a.

Two lines are parallel if they have the same slope.

Thus, we find the equation of a line with:

• Slope, m=a

,

• Point, (x1,y1)=(3,-5)

Using the point-slope form:

$\begin{gathered} y-y_1=m(x-x_1) \\ y-(-5)=a(x-3) \\ y+5=ax-3a \\ y=ax-3a-5 \\ y=ax-(3a+5) \end{gathered}$

The equation of the line is y=ax-(3a+5).