through 2 5 parallel to y 2x 7 Slope of given line Slope

through (2, 5); parallel to y = 2x - 7 Slope of given line: _____ Slope of parallel line: _____ b: _____ line: _____

Solution

Let the equation of the line through the point (2,5) and parallel to the line y = 2x-7 be y = mx+c where m is the slope and c is the y-intercept. Since this line is parallel to the line y = 2x-7, its slope must be 2 so that its equation changes to y = 2x+c. Now, since the line through the point (2,5), on substituting x = 2 and y = 5 in its equation, we get 5 = 2*2+c or, c = 5-4 = 1. Hence, the equation of the required line is y = 2x+1.