Write an equation of the line that passes through the given point and is parallel to the g...

Write an equation of the line that passes through the given point and is parallel to the graph of the given equation. Write the answer in slope-intercept form. See Example.

EXAMPLE Write an equation of the line that passes through (-2, 5) and is parallel to the line y = 8x- 3.

Strategy We will use the point-slope form, y - y1 = m(x — x1), to write the equation of the line.

WHY We know that the line passes through (-2, 5). We can use the fact that the lines are parallel to determine the unknown slope of the desired line.

Solution

Since the slope of the line given by y = 8x- 3 is the coefficient of x, the slope is 8. The desired equation is to have a graph that is parallel to the graph of y = 8x- 3. Its slope must also be 8.

We substitute -2 for x1, 5 for y1, and 8 for m in the point-slope form and simplify.

The equation is y = 8x + 21.

 (−6, 3), y + 3x = −12