Question

Algebra i don't get it

Answer 1

y = 4x + 17

Explanation:

We are to write an equation of the line that is perpendicular to line whose equation is y =
`(1)/(4)` and whose slope is -
`(1)/(4)` = 4

And passes through (-3.5)

The product of slopes of two perpendicular lines is -1

So the slope of the line we are to find is -1 ÷ -
`(1)/(4)` = 4

Taking a point (x,y) on the line we are to find

Slope(m) = Change in y-axis ÷ Change in x-axis

Slope is
`(y - 5)/(x + 3)` = 4

Cross multiplying gives;

y - 5 = 4x + 12

Simplifying gives the equation of our second line;

y = 4x + 17

Answer 2

y = 4x+17, or choice #3

Explanation:

The slope of the line given is -1/4. The slope of a line perpendicular to the original line has a slope that is the negative reciprocal of -1/4, which is 4. The product of the perpendicular and the original slope must be -1, so to check: 4*(-1/4)=-1.

So far we have y = 4x+b for the perpendicular line. The bias b can be determined using the point given, (-3,5):

5 = 4(-3) + b ==> b = 17

Therefore, the equation of the line perpendicular to the line given is:

y = 4x+17, or choice #3