Question

Write an equation of the line passing through the point (-10,3) that is parallel to the line 5x+2y=12

Answer 1

The equation of the line passing through the point (-10,3) parallel to the line 5x+2y=12 is y = (-5/2)x - 22 since parallel lines have the same slope, which in this case is -5/2.

Step-by-step explanation:

To write an equation of a line that is parallel to the given line 5x+2y=12, we first need to find the slope of the given line. Any line parallel to this will have the same slope. Let's start by rewriting the given equation in slope-intercept form, which is y = mx + b where m represents the slope and b is the y-intercept.

5x + 2y = 12

2y = -5x + 12

y = (-5/2)x + 6

The slope of the given line is -5/2. Therefore, the slope of the line we wish to find will also be -5/2 since parallel lines have identical slopes.

Now, using the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can substitute the point (-10,3) and the slope -5/2 into this formula:

y - 3 = (-5/2)(x - (-10))

y - 3 = (-5/2)(x + 10)

y - 3 = (-5/2)x - 25

To make this the slope-intercept form, we solve for y:

y = (-5/2)x - 22

Therefore, the equation of the line passing through (-10,3) parallel to the line 5x + 2y = 12 is y = (-5/2)x - 22.

Answer 2

y= (-5/2)x - 22

because 5x+2y=12 turns to y=(-5/2)x + 6 and the line parallel to it has to have the same slope so you have to just get the y intercept by plugging in -10 into the equation (-5/2)(-10)+?=3 and ?= -22.