How do you write an equation of a line that passes through a point and i parallel to the line with the given i’m so confused and i have a test tomorrow

The equation y = x - 12 is only there to give you the slope. To write an equation of a line that is parallel to the given equation, the slopes have to be the same. (If the equation of a line is PERPENDICULAR to the given equation, the slope would be the opposite. For example, if the slope is positive 4, the new slope would be -1/4. If the slope is -2, the new slope is 1/2.)

You are using the equation y = mx + b

where m = slope, b = y-intercept

Since you know the slope of the given equation is just 1, you plug in 1 for m.

y = 1x + b or y = x + b

With the point P(10,3), you just plug it in to y = x + b to find "b" or the y-intercept.

3 = 10 + b

-7 = b

Your new equation is y = x - 7

if x decreases by 4 then y increases by 10

step-by-step explanation: