Question

What equation is best represented by the graph

Answer 1

Answer: hope this helps ♡

Equation c. 4x-6y=24 is best represented by the graph.

Explanation:

The gradient of a line: y=mx+c

a. 4x - 6y = -24

→ -6y = -4x - 24

→ -6y/-6 = (-4x - 24)/-6

→ y = 2/3x + 4 (-4x/-6 = 4/6x = 2/3x)
a. incorrect bcz the y-intercept here is +4 while the y-intercept on the graph is -4

b. 6x - 4y = 24

→ -4y = -6x + 24

→ -4y/-4 = (-6x + 24)/-4

→ y = 3/2x - 6 (-6x/-4 = 6/4x = 3/2x)
b. incorrect bcz the y-intercept here is -6 while the y-intercept on the graph is -4.

c. 4x - 6y = 24

→ -6y = -4x + 24

→ -6y/-6 = (-4x + 24)/-6

→ y = 2/3x - 4 (-4x/-6 = 4/6x = 2/3x)
c. correct bcz the y-intercept here is -4 while the y-intercept on the graph is -4.

Answer 2

Answer: c) 4x - 6y = 24

Explanation:

First, we will write a slope-intercept form equation to answer this question. We will use the points (0, -4) and (6, 0).

Slope:

`\displaystyle (y_(1) -y_(2) )/(x_(1) -x_(2) ) =(0--4)/(6-0)=(4)/(6)=(2)/(3)`

Point-slope form equation:

y - y1 = m(x - x1)

y - - 4 =
`(2)/(3)`(x - 0)

y + 4 =
`(2)/(3)`x

y =
`(2)/(3)`x - 4

Next, we will transform the given options into slope-intercept form.

a) 4x - 6y = -24 ➜
`y=-(2)/(3) +(5)/(3)` ✗

b) 6x - 4y = 24 ➜
`y=(3)/(2y) x-6` ✗

c) 4x - 6y = 24 ➜
`y=(2)/(3) x-4` ✓

d) 4x + 6y = 24 ➜
`y=-(2)/(3) x+4` ✗