Question

Line parallel to y=0.5x+3 that passes through the point (−9,12)

Answer 1

Considering the expression of a line, the equation of the parallel line is y= 0.5x +16.5.

Linear equation

A linear equation o line can be expressed in the form y = mx + b

where

• x and y are coordinates of a point.
• m is the slope.
• b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.

Parallel line

Parallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.

Two lines are parallel if they have the same slope and different y-intercepts. That is, they have the same value of m and different value of b.

Equation of parallel line in this case

In this case, the line is y=0.5x+3, where

• the slope is 0.5
• the ordinate to the origin is 3.

Two lines are parallel if they have the same slope. So, in this case, the parallel line has a slope of 0.5

Considering point (-9,12) and the slope m, you obtain:

12= 0.5×(-9) + b

12= -4.5 + b

12 + 4.5= b

16.5= b

The equation of the parallel line is y= 0.5x +16.5.

Answer 2

Complete question is;

Write the equation of line in slope-intercept form. Line parallel to y = 0.5x + 3 that passes through the point (−9,12)

Answer:

y - 12 = 0.5(x + 9)

Explanation:

We want to find the line parallel to y = 0.5x + 3 that passes through the point (−9,12).

To some this, we will use the equation;

y - y1 = m(x - x1)

Here, x1 = -9, y1 = 12, m = 0.5

Thus;

y - 12 = 0.5(x - (-9))

y - 12 = 0.5(x + 9)