Find an equation of the line through point (0.5, 3)and parallel to y= -2x + 3.

Question

Find an equation of the line through point (0.5, 3)and parallel to y= -2x + 3.

Answer 1

Hi Rebecca,

Parallel lines have the same slope. When the equation of a line is written in slope-intercept form, the variable, m, represents the slope: y = mx + b

For the equation given in your problem (y = -2x + 3), the slope is -2.

Therefore, the slope of any parallel line will be -2.

To find the equation of the parallel line passing through (0.5, 3), substitute these values for x and y and solve for the y intercept , b, of the parallel line:

y = -2x + b

3 = -2 • 0.5 + b

3= -1 + b

3 + 1 = -1 + b + 1

4 = b

The equation of the line parallel to y = -2x + 3 will be:

y = -2x + 4