Question

Indicate in standard form the equation of the line passing through the given points,

M(0,6),N(6,0).

a) y=−x+6
b) y=x+6
c) y=−x−6
d) y=x−6

Answer 1

The equation of the line in standard form passing through M(0,6) and N(6,0) is found by calculating the slope from these points, which is -1, and using point M to identify the y-intercept, which is 6. Thus, the equation is y = -x + 6, making option a) correct.

Step-by-step explanation:

To find the equation of the line in standard form passing through the points M(0,6) and N(6,0), we can use the two points to determine the slope of the line (m) and then use one of the points to solve for the y-intercept (b). The slope (m) is calculated by the change in y over the change in x, which is (6 - 0) / (0 - 6). This gives us a slope of -1.

The y-intercept (b) is the y-value when x is 0, which we can directly see from point M is 6. Thus, using the slope-intercept form (y = mx + b), we substitute m = -1 and b = 6 to get the equation of the line y = -1x + 6 or y = -x + 6 in standard form.

So, the correct option is a) y = -x + 6.