Question

line r in the xy - plane has a slope of 4 and passes through the point (0, 6). which equation defines line r?
a ( y = - 6x + 4 )
b ( y = 6x + 4 )
c ( y = 4x - 6 )
d ( y = 4x + 6 )

Explanation:

Step1: Recall slope-intercept form

The slope-intercept equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step2: Substitute given slope

The slope $m = 4$, so the equation becomes $y = 4x + b$.

Step3: Solve for y-intercept $b$

The line passes through $(0,6)$, which is the y-intercept, so $b = 6$. Substitute $b$ into the equation: $y = 4x + 6$.

Answer:

D. $y = 4x + 6$