Question

What is the equation of the line in slope-intercept form that passes through point (1,2) and is parallel to the line y = 3x – 2?

Answer 1

The equation of the line parallel to y = 3x - 2 and passing through (1,2) is y = 3x - 1. This is found by using the same slope as the given line, which is 3, and finding the y-intercept by plugging in the coordinates of the given point into the slope-intercept equation.

Step-by-step explanation:

The equation of the line in slope-intercept form that passes through point (1,2) and is parallel to the line y = 3x – 2 can be found using the fact that parallel lines have equal slopes. Given that the slope of the given line is 3 (the coefficient of x in the equation), the slope (m) of our new line will also be 3. To find the y-intercept (b), we use the point that the line passes through, (1,2).

By substituting the given point into the slope-intercept form equation y = mx + b, we get:
2 = 3(1) + b => 2 = 3 + b => b = -1.
So, the equation of our line is y = 3x - 1.

Answer 2

The equation of the line in slope-intercept form that passes through the point (1,2) and is parallel to the line y = 3x – 2 is y = 3x - 1.

Step-by-step explanation:

In slope-intercept form, the equation of a line is given by y = mx + b, where m is the slope and b is the y-intercept. The given line has a slope of 3, which means any line parallel to it will also have a slope of 3.

To find the equation of the parallel line passing through the point (1,2), we substitute the coordinates (x, y) = (1,2) into the equation and solve for the y-intercept (b). Substituting these values into the equation, we get 2 = 3(1) + b. Solving for b gives us b = -1.

Therefore, the equation of the line parallel to y = 3x - 2 and passing through the point (1,2) is y = 3x - 1. This line has a slope of 3, similar to the original line, but a different y-intercept, reflecting the shift to pass through the given point.