Select the equation in which the graph of the line has a positive slope, and the y-intercept equals -8.
Question 1 options:
5x + y = 50
5x - 10y = -12
x - 2y = 10
10x - 5y = 40
first step: which have positive slopes?
a , c and d @steve
no, (a) has a negative slope. Rearrange things into slope-intercept form and you get
5x + y = 50
y = -5x+50
slope = -5, intercept=50
do that for the others, and it will then be clear which is what you want.
To determine the equation of a line with a positive slope and a y-intercept of -8, we need to find an equation in slope-intercept form: y = mx + b, where m represents the slope and b represents the y-intercept.
Let's analyze the given options:
Option 1: 5x + y = 50
This equation is not in slope-intercept form, so we will need to rearrange it. Subtracting 5x from both sides, we get y = -5x + 50. The slope of this equation is -5, not positive, so we can eliminate this option.
Option 2: 5x - 10y = -12
Similar to the previous option, this equation is not in slope-intercept form. Let's rearrange it. Subtracting 5x from both sides and then dividing the whole equation by -10, we get y = 0.5x + 1.2. The slope of this equation is 0.5, not positive, so we can eliminate this option too.
Option 3: x - 2y = 10
Again, this equation is not in slope-intercept form. Let's rearrange it. Subtracting x from both sides and then dividing the whole equation by -2, we get y = -0.5x - 5. The slope of this equation is -0.5, not positive, so we can eliminate this option as well.
Option 4: 10x - 5y = 40
Like the previous options, this equation is not in slope-intercept form. Let's rearrange it. Subtracting 10x from both sides and then dividing the whole equation by -5, we get y = 2x - 8. The slope of this equation is 2, which is a positive value, and the y-intercept is -8, as required.
Therefore, the equation in which the graph of the line has a positive slope and a y-intercept of -8 is 10x - 5y = 40.