which equation is parallel to the graph of the equation 4x+y=-2 and passes through the point (5,3)?
put the equation into slope intercept form
y=-4x-2
the slope is -4
the equatio of the new line is
y=-4x+b
Put x,y of the point into this and solve for b, and then you have then new line.
Here is another very easy way:
Your new equation will only differ in the constant, so it must be 4x+y=c
put in (5,3), 20+3=c
so your equation is 4x+y=23
To find an equation that is parallel to a given equation and passes through a specific point, you need to follow these steps:
1. Determine the slope of the given equation.
2. Use the slope to construct the equation with the point provided.
Let's apply these steps to the equation 4x + y = -2 and the point (5, 3):
Step 1: Determine the slope of the given equation.
To find the slope, rearrange the equation in slope-intercept form (y = mx + b), where m represents the slope:
4x + y = -2
y = -4x - 2
From this, we can see that the slope of the original equation is -4.
Step 2: Use the slope to construct the equation with the given point.
Using the point-slope formula (y - y1 = m(x - x1)), substitute the values of the point (5, 3) and the slope (-4) into the equation:
y - 3 = -4(x - 5)
Now, you can simplify this equation to find the final answer:
y - 3 = -4x + 20
y = -4x + 23
Therefore, the equation parallel to 4x + y = -2 and passes through the point (5, 3) is y = -4x + 23.