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.
(0, 0), y = 4x −7
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