Final answer:
The slope-intercept form for the line parallel to y=4x+6 that goes through the point (1,-3) is y = 4x - 7, as parallel lines share the same slope and the y-intercept can be calculated using the point (1,-3) with this slope.
Step-by-step explanation:
The question is asking to find the slope-intercept form equation of a line parallel to y=4x+6 passing through the point (1,-3). Lines that are parallel have the same slope. Hence, the slope (m) of the new line will be the same as the slope of the given line, which is 4.
To find the y-intercept (b) of the new line, we use the point-slope form and we substitute the known point and slope:
y - y₁ = m(x - x₁)
Substituting the given point (x₁,y₁) = (1, -3) and m = 4,
y - (-3) = 4(x - 1)
y + 3 = 4x - 4
y = 4x - 7
Therefore, the equation in slope-intercept form for the line parallel to y=4x+6 going through the point (1, -3) is y = 4x - 7, which corresponds to option B.