Write your answer in standard form with integer coefficients.
1. (-5, 2); m = 2/5
2.(-6, -1); m=-4
how do i do this?
I would do this. The straight line formula is
y = mx + b
m = 2/5 and you want the line to go through the point x=-5 and y = 2; therefore, substitute those values for x and y. I'll let you do the work but I get b = 4 and the equation then looks like this.
y = (2/5)x + 4. The problem asks for integers so multiply through by 5.
5y = 2x + 20
CHECK:
5(2) = 2(-5) + 20
10 = -10 + 20
20 = 20 so it checks.
To write the equation of a line in standard form with integer coefficients, you need to use the slope-intercept form (y = mx + b) of the equation and rearrange it.
Given the points (-5, 2) and the slope m = 2/5 in the first question, you can substitute these values into the slope-intercept form to get the equation of the line.
Start by substituting the values of x and y from the given point (-5, 2) into the equation:
2 = (2/5)(-5) + b
Now, simplify the equation:
2 = -2 + b
To isolate the variable b, add 2 to both sides of the equation:
2 + 2 = -2 + b + 2
4 = b
Therefore, the y-intercept is b = 4. Now you can substitute the values of m and b into the slope-intercept form to get the equation:
y = (2/5)x + 4
To convert this equation into standard form with integer coefficients, you need to eliminate fractions and make sure the coefficients are integers.
Multiply the entire equation by 5 to eliminate the fraction:
5y = 2x + 20
Now, rearrange the equation so the x and y terms are on the same side:
2x - 5y = -20
This equation is in standard form with integer coefficients.
Now, let's move on to the second question: (-6, -1) with a slope of m = -4.
Using the same process, substitute the values of x and y into the slope-intercept form:
-1 = -4(-6) + b
Simplify the equation:
-1 = 24 + b
To isolate the variable b, subtract 24 from both sides of the equation:
-1 - 24 = 24 + b - 24
-25 = b
Therefore, the y-intercept is b = -25. Now substitute the values of m and b into the slope-intercept form:
y = -4x - 25
Multiply the entire equation by -1 to eliminate the negative sign:
-y = 4x + 25
Rearrange the equation:
4x + y = -25
This equation is in standard form with integer coefficients.
So, the answer to the first question is 2x - 5y = -20, and the answer to the second question is 4x + y = -25.