Question

What is the equation, in slope-intercept form, of the line parallel to ​y=5x+2 that passes through the point with coordinates (−2,1)?

Answer 1

The equation of line parallel to ​y=5x+2 that passes through the point with coordinates (−2,1) is:

$y=5x+11$

Step-by-step explanation:

Given line is:

y=5x+2

Given equation is in slope-intercept form, the coefficient of x will be the slope of line

So slope is 5

As parallel lines have equal slopes the required line will also have slope 5.

Slope-intercept form is:

y=mx+b

Putting the value of slope

y=5x+b

To find the value of b, putting (-2,1) in equation

$1=(5)(-2)+b\\1=-10+b\\b=1+10\\b=11$

Putting the values of b and m

$y=5x+11$

The equation of line parallel to ​y=5x+2 that passes through the point with coordinates (−2,1) is:

$y=5x+11$

Keywords: Equation of line, Slope-intercept form

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Answer 2

Here, we are required to find an equation, in slope-intercept form, of the line parallel to

y = 5x +2 that passes through the point with coordinates (−2,1).

• The equation is , y = 5x + 11.

Mathematically, the slope of 2 parallel lines are equal: i.e M1 = M2.

By comparison with the equation of a straight line (y = mx + c);

The slope of the line y = 5x + 2 is; m1 = 5.

Therefore, the slope of the second line is also 5 and passes through the point (-2,1). As such, the equation of the line is given as;

5 = (y - 1)/(x - (-2))

5 = (y - 1)/(x + 2)

By cross product;

5x +10 = y - 1

y = 5x +11

The equation is therefore, y = 5x + 11.

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