Answer:
5x - 2y = -20
Step-by-step explanation:
We are given that:
- a line passes through (-2, 5)
- this line has a slope of 5/2
We want to write the equation of this line in ax+by=c form, where a, b, and c are integers. This is known as standard form
But before we do that, we first need to write the equation of the line in a different format; for example, in slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept
As we are already given the slope, we can immediately plug it into the formula.
Substitute 5/2 as m in the equation:
y = 5/2x + b
Now we need to find b
As the point passes through the point (-2,5), we can use its values to help solve for b
Substitute -2 as x and 5 as y:
5 = 5/2(-2) + b
Multiply
5 = -5 + b
Add 5 to both sides
10 = b
Substitute 10 as b into the equation
y = 5/2x + 10
This is the equation in slope-intercept form. However, remember that we want it in standard form
As standard form has both variables on one side, we can move the term containing x to the left side
Subtract 5/2x from both sides
-5/2x + y = 10
Remember that the values of a, b, and c must be integers (whole numbers). Also, an additional rule is that a (the coefficient in front of x) cannot be negative.
So multiply both sides by -2 to clear the fraction & to change the sign of a
-2(-5/2x + y) = -2(10)
Multiply
5x - 2y = -20
Topic: standard form
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