Select the equation in which the graph of the line has a positive slope, and the y-intercept equals -8.
Question 1 options:
x - 2y = 10
10x - 5y = 40
5x + y = 50
5x - 10y = -12
The slope of a line Ax+By=C is given by -A/B.
Therefore if A & B have different signs, the slope is positive.
This will help you eliminate the third equation, since coefficients of x and y have the same sign, therefore negative slope.
Now set x=0 in each of the equations and solve for y. The result is the y-intercept. Select the equation that gives y-intercept=-8.
To find the equation with a positive slope and a y-intercept of -8, we need to look for the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Let's analyze the options:
1. x - 2y = 10: This equation is not in slope-intercept form. Let's rewrite it in that form: -2y = -x + 10 → y = (1/2)x - 5. In this equation, the slope is (1/2), which is positive. However, the y-intercept is -5, not -8.
2. 10x - 5y = 40: This equation is not in slope-intercept form. Let's rewrite it: -5y = -10x + 40 → y = 2x - 8. The slope in this equation is 2, which is positive, and the y-intercept is -8. Therefore, this is the correct equation.
3. 5x + y = 50: This equation is not in slope-intercept form. Let's rewrite it: y = -5x + 50. In this equation, the slope is -5, not positive.
4. 5x - 10y = -12: This equation is not in slope-intercept form. Let's rewrite it: -10y = -5x - 12 → y = (1/2)x + (6/5). In this equation, the slope is (1/2), which is positive. However, the y-intercept is (6/5), not -8.
Therefore, the equation with a positive slope and a y-intercept of -8 is 10x - 5y = 40.
To find the equation of a line with a positive slope and a y-intercept of -8, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
The equation we are looking for must have a positive slope, which means that the coefficient of x should be positive.
Let's go through the given options one by one:
1. x - 2y = 10:
2y = x - 10
y = (1/2)x - 5
The coefficient of x is positive (1/2), but the y-intercept is -5, not -8, so this equation is not the right one.
2. 10x - 5y = 40:
5y = 10x - 40
y = 2x - 8
The coefficient of x is positive (2), and the y-intercept is -8, so this equation matches the given conditions.
3. 5x + y = 50:
y = -5x + 50
The coefficient of x is negative (-5), so this equation does not have a positive slope.
4. 5x - 10y = -12:
10y = 5x + 12
y = (1/2)x + (6/5)
The coefficient of x is positive (1/2), but the y-intercept is 6/5, not -8, so this equation is not the right one.
Therefore, the equation with a positive slope and a y-intercept of -8 is 10x - 5y = 40.