Question

The equation of a line is y = 3x − 5. Write down the slope of this line and the intercept made by it on the Y-axis. Hence, or otherwise, write down the equation of a line which is parallel to the line and which passes through the point (0, 5).

Answer 1

The given equation is y = 3x − 5, and it is already in the slope-intercept form y = mc + x, where:

Slope (m) = 3

Y-intercept (c) = −5

Since the line is parallel to y = 3x − 5, so it have the same slope:

Parallel slope (m_p) = 3coordinate is

The new line passes through the point (0, 5). Since the x-coordinate is 0, the new y-intercept (c_p) is 5.

Using the slope-intercept form y = m_px + c_p:

y = 3x + 5

Hence, the slope = 3, Y-intercept = −5 and the equation of the parallel line = y = 3x + 5 or 3x − y + 5 = 0.