Write the equation of the line, in standard form, that passes through the points (-2, 2) and (4, 5). Show all work for credit.

x - 2y + 6 = 0  

Step-by-step explanation:

Going from (-2, 2) to (4, 5), we see that x (the 'run') increases by 6 and that y (the 'rise') increases by 3.  Thus, the slope of the line through these two points is m = rise / run = 3/6, or m = 1/2.

Starting with the slope-intercept formula y = mx + b, and using the x and y values from the point (-2, 2), we get

2 = (1/2)(-2) + b, or 4 = -2 + 2b, or 6 = 2b, or b = 3.  Then the slope-intercept form of the desired equation is y = (1/2)x + 3.  To obtain the standard form, we multiply all three terms of this result by 2, obtaining 2y = x + 6, or

x - 2y + 6 = 0                                                                        

b. 24 mm

step-by-step explanation:

use the pythagorean theorem.

a^2 + b^2 = c^2

a^2 + 7^2 = 25^2

a^2 + 49 = 625

a^2 = 576

a = 24

answer: b. 24 mm