I need help solving this problem.

Mathematics

1 answer:

Galina-37 [17]4 years ago

3 0

Answer:

y = $\frac{1}{4}$ x - $\frac{9}{2}$

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 4x + 38 is in this form with slope m = - 4

The line ST is perpendicular to line RS ( angles in a square are 90° )

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-4}$ = $\frac{1}{4}$

y = $\frac{1}{4}$ x + c ← is the partial equation

To find c substitute (2, - 4) into the partial equation

- 4 = $\frac{1}{2}$ + c ⇒ c = - 4 - $\frac{1}{2}$ = - $\frac{9}{2}$

y = $\frac{1}{4}$ x - $\frac{9}{2}$ ← equation of ST

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A line the contains the point (-3,6) and (5,10)

wlad13 [49]

Ok so for slope it's difference in y dividing by the difference of x. The difference of y is 10 - 6 which is 4, and the change in x is 5 - (-3) which is 8. Dividing 4 by 8 gets us 1/2. So the slope is 1/2. Slope intercept form would be y = mx + b, and the slope is 1/2 so it'd be y = (1/2)x + b. Plug in a point and you get b = 15/2. So the final slope intercept form would be y = (1/2)x + 15/2. For point slope form just put in a point and slope and you get y - 6 = (1/2) × (x + 3). Standard form would have to be arranged from slope intercept. So multiplying 2 to the slope intercept form we get 2y = x + 15. Subtracting x we get -x + 2y = 15. In standard form we don't want x to be negative so just multiply by negative one and we get x - 2y = -15.