Question

Line J passes through the point (2, 10) and has a gradient of 3.

Line I can be translated to give line K, which passes through the point (2, 11).
a) Work out the coordinates of the y-intercept of line J.
b) By comparing line J and line K, write down the coordinates of the y-intercept of line K.

Answer 1

The y-intercept of line J is (0, 4) by applying the point-slope form with the given point and slope. Line K, being a vertical translation of line I, has the same slope as J and passes through (2, 11), thus its y-intercept is (0, 5), one unit above J's intercept.

Step-by-step explanation:

To work out the coordinates of the y-intercept of line J, which passes through the point (2, 10) and has a gradient (slope) of 3, we can use the slope-intercept form of a line's equation: y = mx + b, where m is the slope and b is the y-intercept.

Since the line passes through (2, 10) and has a slope of 3, we can substitute these into the equation to find b.

y = mx + b
10 = (3)(2) + b
10 = 6 + b
b = 4

Therefore, the y-intercept of line J is (0, 4).

To find the coordinates of the y-intercept of line K, which can be translated from line I, and knowing that line K passes through the point (2, 11), we just need to recognize that a vertical translation does not affect the slope of a line.

Since the original line J has a y-intercept of (0, 4) and line K is one unit above line J at the given x-coordinate of 2, we can conclude that line K's y-intercept is also one unit above line J's y-intercept, leading to a y-intercept for line K of (0, 5).