Write an equation in slope-intercept form for the line perpendicular to y=−4x+1 that passes through the point (−7,1).

y = (1/4)x + (11/4)

Step-by-step explanation:

A perpendicular line equation has a slope that is the negative inverse of the reference line, in this case y = -4x + 1.

This means we want a new that that has a slope of -(-1/4) or (1/4).

That leads to:

y = (1/4) + b

Any value of b will still yield a straight, but perpendicular line.  But the question is more particular, like a difficult spouse.  It wants to go through the point (-7,1).  We can make that happen by setting a value for by that will move the line such that it crosses (-7,1).  Substitute that point in the equation and solve for b:

y = (1/4)x + b

1 = (1/4)(-7) + b

b = 1 +(7/4)

b = (4/4 + 7/4)

b = (11/4)

The equation becomes y = (1/4)x + (11/4)

See attachment.

answer:

given the linear inequality :

add 2y to both sides we get;

simplify:

add 12 to both sides of an equation;

simplify:

divide both sides by 2 we get;

or

the related equation for the inequality equation [1] is;

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

subtract 6 from both sides we get

multiply both sides by 2 we get;

or

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.