The graph of a line has a slope of -7 and a y intercept of (0,0). rewrite the equation in standard form (ax+by=c) with a positive x-term. a, b, and c must all be interger

the equation of the line is 7x + y = 0 .

Step-by-step explanation:

in the standard form of the line that is Ax +By = C we can write it in the form of

By = C - Ax

which is in the form of

where m is the slope of the line and c is y intercept made by the line.

comparing   and  

we get that and

since it is given that slope of the line is -7 therefore m = -7 and c = 0

therefore   and

therefore C = 0 , A = 7 and B = 1

therefore the equation becomes 7x + y = 0

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!