Write y=−25x+2
in standard form using integers.
(1 point)
Responses
2x + 5y = 10
2x + 5y = 10
2x + 5y = -10
2x + 5y = -10
2x - 5y = 10
2x - 5y = 10
2x - 5y = -10
2x + 5y = -10
Write an equation for the line that is parallel to the given line and passes through the given point.
y = 2x + 3; (-3, -1)
(1 point)
Responses
y = -1/2x + 5
y = -1/2x + 5
y = -2x + 5
y = -2x + 5
y = 2x +7
y = 2x +7
y = 2x + 5
y = 2x + 5
Tell whether the pair of lines are parallel, perpendicular, or neither.
y = 3/4x + 7 and 4x - 3y = 9
(1 point)
The
line y = 3/4x + 7 is in slope-intercept form, where the slope is 3/4.
To determine the slope of the second line 4x - 3y = 9, we can rearrange it into slope-intercept form:
4x - 3y = 9
-3y = -4x + 9
y = 4/3x - 3
The slope of the second line is 4/3.
Since the slopes of the two lines (3/4 and 4/3) are reciprocals of each other, the lines are perpendicular.
To write the equation y = -25x + 2 in standard form, we need to rearrange the terms so that the coefficients of x and y are integers, and the constant term is also an integer.
The given equation is already in slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
To convert this to standard form, we need to eliminate the fraction. We can do this by multiplying the entire equation by a common denominator, which, in this case, is 100, since the fraction is -25/1:
100y = -25(100x) + 2(100)
Simplifying:
100y = -2500x + 200
Now, let's rearrange the equation so that the x term and the y term are on the same side:
2500x + 100y = 200
Divide both sides of the equation by 100 to simplify and make the coefficient of x positive:
25x + y = 2
So, the standard form of the equation y = -25x + 2 is 25x + y = 2.