Final answer:
To express the line with a point (1,2) and slope of 3 in slope-intercept form, we substitute the values into y = mx + b to find 'b' and obtain the equation y = 3x - 1.
Step-by-step explanation:
To solve the mathematical problem completely, we must write the equation of a line given a point and a slope in slope-intercept form, which is y = mx + b. The given point is (1,2) and the slope (m) is 3. We can substitute the known values into the slope-intercept form to find b, the y-intercept.
The equation is:
y - y1 = m(x - x1)
y - 2 = 3(x - 1)
Distributing the slope on the right side, we get:
y - 2 = 3x - 3.
Add 2 to both sides to isolate y:
y = 3x - 1.
Thus, the equation in slope-intercept form is y = 3x - 1.