Question

Alejandro correctly wrote the equation y - 3 = (1/5)(x - 10) to represent a line that his teacher sketched. The teacher then changed the line so it has a slope of two but still went through the same point. Which equation should Alejandro write to represent the new line?

A) y - 3 = 2(x - 10)
B) y - 3 = (2/5)(x - 10)
C) y - 3 = (1/2)(x - 10)
D) y - 3 = (2/1)(x - 10)

Answer 1

To represent a line with a slope of two that passes through the same point, Alejandro should write the new equation as A) y - 3 = 2(x - 10), changing the original slope to two.

Step-by-step explanation:

The student is asked to write a new equation for a line that still passes through the point (10, 3) but now has a different slope of two. The original equation was y - 3 = (1/5)(x - 10). The only change that needs to be made to the original equation is to update the slope (m) to the new slope of two, while keeping the same structure of the equation and the point it passes through intact. Therefore, the correct new equation that Alejandro should write is:

A) y - 3 = 2(x - 10)

Each of the other options given has the incorrect slope value for the line. Understanding that the slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept, helps in identifying the correct option where only the m term is changed to two.