What is the slope-intercept form of the line passing through (1, 2) with a slope of 3?

To find the slope-intercept form of a line, which is expressed as ( y = mx + b ), you need two key pieces of information: the slope ( m ) and the y-intercept ( b ). In this case, you have a slope of 3 and a point the line passes through, which is (1, 2).

Start with the slope-intercept formula:

[ y = mx + b ]

Substituting in the known slope:

[ y = 3x + b ]

Next, use the coordinates of the point (1, 2) to find ( b ). Substitute ( x = 1 ) and ( y = 2 ) into the equation:

[ 2 = 3(1) + b ]

[ 2 = 3 + b ]

To solve for ( b ), subtract 3 from both sides:

[ b = 2 - 3 ]

[ b = -1 ]

Now, substitute ( b ) back into the slope-intercept form:

[ y = 3x - 1 ]

This confirms that the correct slope-intercept form of the line that passes through the point (1, 2)