Question

Which equation describes a line parallel to y= 4x+ 5 through point (-2, 1)?​

Answer 1

Answer:

y= 4x + 9

Step-by-step explanation:

y= 4x+5

y= 4(x+ 5/4)

m, gradient= 4

rule if parallel: their gradients are equal

rule if perpendicular : m1*m2=-1

parallel gradient, m1=4

passes through (-2, 1) so x= -2,  y= 1

y - 1= 4(x -- 2)

y= 4x + 9

Answer 2

The line parallel to y= 4x+ 5 passing through point (-2, 1) is y = 4x + 9

Parallel Equations

The given equation is:

y = 4x + 5

Compare y = 4x + 5 with the equation y = mx + c

m = 4, c = 5

The equation parallel to y = 4x + 5 will also have a slope, m = 4

The point-slope form of the equation of a line is given as:

y - y₁ = m(x - x₁)

substitute m = 4, x₁ = -2 and y = 1 into the equation above

y - 1 = 4(x - (-2)

y - 1 = 4(x + 2)

y - 1 = 4x + 8

y = 4x + 8 + 1

y = 4x + 9

Therefore the line parallel to y= 4x+ 5 passing through point (-2, 1) is y = 4x + 9

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