Find the equation of a line that passes through (2,14) and is parallel to the graph of y = 3x + 4.
Write the equation in slope – intercept form.
Solution:-
If the slope and a point on the line are known, we can find the equation of the line on slope-intercept form.
Parallel lines have the same slope. Therefore, the slope of the line that is parallel to the given line, y = 3x + 4, is 3.
Find the equation of the line that passes through the point (2,14) with a slope of 3. Substitute 2 for x1, 14 for y1, and 3 for m into the point-slope form.
y – y1 = m(x- x1)
y – 14 = 3 (x-2)
Solve the equation for y.
y – 14 = 3(x – 2)
y = 14 = 3x – 6
y = 3x + 8
Thus, the equation of the desired line is y = 3x + 8.