Question

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

L(5, 0), M(0, 5)

Answer 1

first we find the slope with the slope formula :
slope(m) = (y2 - y1) / (x2 - x1)
(5,0) x1 = 5 and y1 = 0
(0,5) x2 = 0 and y2 = 5
now we sub
slope(m) = (5 - 0) / (0 - 5)
slope(m) = 5/-5
slope(m) = -1

now we use y = mx + b
slope(m) = -1
you can use either set of points, answer will come out the same
(5,0) x = 5 and y = 0
now lets sub
0 = -1(5) + b
0 = -5 + b
5 = b
your equation in slope intercept form is :
y = -x + 5
but we want this in standard form
add x to both sides
x + y = 5 ===> this is standard form

Answer 2

Thanks I kinda get it you explaine every well could you help me with a cupple more ?

Answer 3

Indicate the equation of the given line in standard form.

The line through (2, -1) and parallel to a line with slope of 3/4

Answer 4

a parallel line will have the same slope, so the slope we need is 3/4.

y = mx + b
(2,-1) x = 2 and y = -1
slope(m) = 3/4
now lets sub and solve for b
-1 = 3/4(2) + b
-1 = 3/2 + b
-1 - 3/2 = b
-2/2 - 3/2 = b
-5/2 = b
equation in slope intercept form is :
y = 3/4x - 5/2 --- multiply by the LCD, which is 4
4y = 3x - 10 -- subtract 3x from both sides
-3x + 4y = -10 -- multiply by -1 to make x positive
3x - 4y = 10 ===> standard form

Answer 5

thank you :) so much