Find an equation for a line that contains (-4, -3) and is parallel to the graph of 2x - 5y = 40
1. y = -2/5 x + 4 3/5
2. y = 2/5 x - 1 2/5
3. y = -5/2x - 13
4. y = 5/2x + 7
2x - 5y = 40 has slope 2/5
So, now you have a point and a slope, so use the point-slope form of the line:
y+3 = 2/5 (x+4)
Now pick the choice which matches that
P(-4,-3), m = -A/B = -2/-5 = 2/5.
Y = mx+b.
-3 = (2/5)(-4) + b,
b = ?
Plug the calculated value of m and b into the above equation.
To find an equation for a line that is parallel to the graph of 2x - 5y = 40, we need to determine the slope of the given line. The equation is already in the standard form, Ax + By = C. We can rewrite it in slope-intercept form, y = mx + b, where m represents the slope.
First, let's isolate y in the equation 2x - 5y = 40:
-5y = -2x + 40 (subtract 2x from both sides)
y = (2/5)x - 8 (divide both sides by -5)
The slope of the given line is 2/5. Since lines that are parallel have the same slope, the slope of the line we're looking for is also 2/5.
Now that we have the slope, we can use the point-slope form of a linear equation, which is: y - y₁ = m(x - x₁), where (x₁, y₁) represents a point on the line.
Given the point (-4, -3), we can substitute the values into the point-slope form:
y - (-3) = (2/5)(x - (-4))
y + 3 = (2/5)(x + 4)
Simplifying further:
y + 3 = (2/5)x + (2/5)4
y + 3 = (2/5)x + 8/5
y = (2/5)x + 8/5 - 3
y = (2/5)x + 8/5 - 15/5
y = (2/5)x - 7/5
Therefore, the equation for the line that is parallel to 2x - 5y = 40 and passes through (-4, -3) is option 2: y = (2/5)x - 1 2/5.