write an equation in point slope from fro the line through the given point with the given slope (-3, -5); m = -2/5
The point-slope form of an equation for a line is given by:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
Given that the point is (-3, -5) and the slope is m = -2/5, the equation in point-slope form becomes:
y - (-5) = (-2/5)(x - (-3))
Simplifying further:
y + 5 = (-2/5)(x + 3)
write y = -0.6x + 0.2 in standered form using integers
To convert the equation y = -0.6x + 0.2 to standard form using integers, we need to eliminate the decimal by multiplying the entire equation by 10.
10y = -6x + 2
Next, we can rearrange the equation so that the variables are on one side and the constant term is on the other side:
6x + 10y = 2
Finally, by dividing all terms by their greatest common divisor (which is 2 in this case), we can further simplify the equation to have integer coefficients:
3x + 5y = 1
Therefore, the equation y = -0.6x + 0.2 in standard form using integers is 3x + 5y = 1.
Tell whether the lines for each paor of equations are parallel, perpendicular, or neither
y = -4x + 3
-2 + 8y = 5
To determine if the lines are parallel, perpendicular, or neither, we need to compare their slopes.
The given equation y = -4x + 3 is in slope-intercept form, y = mx + b, where m represents the slope of the line. In this case, the slope is -4.
To find the slope of the second equation, -2x + 8y = 5, we need to rearrange it into slope-intercept form.
-2x + 8y = 5
8y = 2x + 5
y = (2/8)x + 5/8
y = (1/4)x + 5/8
Comparing the slopes, we see that the slope of the second equation is 1/4.
Since the slopes are not equal or negative reciprocals of each other, the lines are neither parallel nor perpendicular.