Find the slope and y-intercept that has infinite solutions to the equation
-18x + 2y = 36
To determine the slope and y-intercept of an equation, we need to rewrite it in slope-intercept form, which is in the form y = mx + b, where m is the slope and b is the y-intercept.
-18x + 2y = 36
To isolate y, we can rearrange the equation:
2y = 18x + 36
y = 9x + 18
Now, we can see that the slope (m) is 9 and the y-intercept (b) is 18.
However, the equation given -18x + 2y = 36 has infinite solutions, which means that every point on this line satisfies the equation. In other words, there are infinitely many combinations of x and y values that make the equation true.
Therefore, the slope and y-intercept of an equation with infinite solutions is m = 9 and b = 18.
Find the slope and y-intercept that has infinite solutions to the equation
3x + 10y = 20
To find the slope and y-intercept of the equation 3x + 10y = 20, we first need to rearrange the equation in slope-intercept form:
10y = -3x + 20
y = (-3/10)x + 2
Now we can see that the slope (m) is -3/10 and y-intercept (b) is 2.
If an equation has infinite solutions, it means that the graph of the equation is a line that coincides with the line described by the equation. In this case, the slope and y-intercept of the equation are m = -3/10 and b = 2, respectively.
Fill in the blanks so that the following system of linear equations has infinite solutions.
y = -4x + 9
y = _x + _
To create a system of linear equations with infinite solutions, the slopes of the two equations must be equal, and the y-intercepts must be the same or have a relationship.
Looking at the first equation y = -4x + 9, we can see that the slope is -4 and the y-intercept is 9.
To ensure the second equation has the same slope, we can choose any value for the coefficient of x. Let's choose 4 since it has the same magnitude as -4 but is positive.
So, y = 4x + k, where k can be any constant.
To have infinite solutions, the y-intercept of the second equation needs to be the same as the y-intercept of the first equation. The y-intercept of y = -4x + 9 is 9.
Therefore, the second equation is y = 4x + 9.
To find the slope and y-intercept of the equation -18x + 2y = 36, we can rewrite it in slope-intercept form, which is of the form y = mx + b, where m is the slope and b is the y-intercept.
To rewrite the equation in slope-intercept form, we need to isolate y. Let's start by moving the -18x term to the other side of the equation:
-18x + 2y = 36
To move -18x to the other side, we can add 18x to both sides:
2y = 18x + 36
Now, divide both sides of the equation by 2 to isolate y:
y = 9x + 18
Now we can see that the equation is in slope-intercept form, y = mx + b, where m = 9 is the slope and b = 18 is the y-intercept.
Since the slope and y-intercept are both fixed values, there are no infinite solutions to this equation.