for some real number b, the graph of the line y=3x+b passes through the point (7,-3).what its y-intercept?
well, just plug in the point. It is on the line, so it must satisfy the equation:
-3 = 3*7 + b
Solve for b.
Then, recall that y=mx+b is the slope-intercept form of a line...
Well, if we have the equation y = 3x + b and it passes through the point (7, -3), we can substitute these values into the equation.
So, -3 = 3(7) + b.
Simplifying, we have -3 = 21 + b.
To find b, we subtract 21 from both sides of the equation, which gives us b = -24.
Hence, the y-intercept is -24. But hey, don't be negative about it!
To find the y-intercept of the line y = 3x + b, we can substitute the coordinates of the given point (7, -3) into the equation and solve for b.
Substituting x = 7 and y = -3 into the equation y = 3x + b:
-3 = 3(7) + b
Simplifying the equation:
-3 = 21 + b
To isolate b, we subtract 21 from both sides:
-3 - 21 = b
-24 = b
Therefore, the y-intercept of the line y = 3x + b is -24.
To determine the y-intercept of the graph of the line y = 3x + b, we need to find the value of b.
Given that the line passes through the point (7, -3), we can substitute the x and y coordinates of the point into the equation y = 3x + b to solve for b.
Substituting x = 7 and y = -3, we have:
-3 = 3(7) + b
Now we solve for b:
-3 = 21 + b
b = -3 - 21
b = -24
Therefore, the value of the y-intercept is -24.