What is the equation of a line that is perpendicular to the line y = 2x + 4 and passes through the point (-2, 3)?

Step-by-step explanation:

The given equation is written in slope-intercept form:

where:

The slope is 2:

When two lines are perpendicular, their slopes will be opposite reciprocals. Find the slope of the line perpendicular to the given equation:

This can be seen as:

Flip the fraction (reciprocal):

→

Now find the opposite:

→

So the slope of the perpendicular line is:

Now make an equation written in point-slope form:

where:

Insert information:

Simplify to slope-intercept form. Solve for y:

Use the distributive property:

Add 3 to both sides to isolate the variable:

:Done

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

you didn't give an question you just gave us a statement