During a manufacturing process, a metal part in a machine is exposed to varying temperature conditions. The manufacturer of the
machine recommends that the temperature of the machine part remain below 141°F. The temperature T in degrees Fahrenheit x minutes after the machine is put into operation is modeled by T = 0.005x² + 0.45x + 125.
Will the temperature of the part ever reach or exceed 141F? Use the discriminant of a quadratic equation to decide.
A. yes
B. no
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. We know that if 2 lines are parallel to one another, their slopes are exactly the same. So the slope of the new line is 5, just like the slope of the original line. We also have a coordinate in the form of (x, y) to fit into that line equation and solve it for b. Like this: -1 = 5(-6) + b and -1 = -30 + b and b = 29. Now we can rewrite the equation fitting in the given slope and the newly found y-intercept value of 29: y = 5x + 29 is the new line.