Agiven line has the equation 10x + 2y = −2.

what is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)?

The equation is

This case asking the end result in the form of a slope-intercept.

Step-1: find out the gradient.

10x + 2y = -2

We isolate the y variable on the left side. Subtract both sides by 10x, we get:

2y = - 10x - 2  

Divide both sides by two

y = -5x -1

The slope-intercept form is , with the coefficient m as a gradient. Therefore, the gradient is m = -5.

If you want a shortcut to find a gradient from the standard form, implement this:  

10x + 2y = −2 ⇒ a = 10, b = 2

Step-2: the conditions of the two parallel lines

The gradient of parallel lines is the same . So

Final step: figure out the equation, in slope-intercept form, of the parallel line to the given line and passes through the point (0, 12)

We use the point-slope form.

Given that

y - 12 = - 5(x - 0)

y - 12 = - 5x

After adding both sides by 12, the results is

Alternative steps

Substitutes m = -5 and (0, 12) to slope-intercept form

12 = -5(0) + c

Constant c is 12 then arrange the slope-intercept form.

Similar results as above, i.e.

Note:

Keywords: given line, the equation, slope-intercept form, standard form, point-slope, gradien, parallel, perpendicular, passes, through the point, constant

step-by-step explanation: