Question

Indicate the equation of the line, in standard form, that passes through (2, -4) and has a slope of 3/5. Enter your answer into the blank equation box.
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Answer 1

The equation of the line is  $y = (3/5)x + 26/5$

Step-by-step explanation:

• The line passes through the point (2,-4).
• The line has the slope of 3/5.

To find the equation of the line passing through a point and given its slope, the slope-intercept form is used to find its equation.

The equation of the line when a point and slope is given :

⇒ $(y-y1) = m(x-x1)$

where,

• m is the slope of the line.
• (x1,y1) is the point (2.-4) in which the line passes through.

Therefore, the equation of the line can be framed by,

⇒ $(y-(-4)) = 3/5 (x-2)$

⇒ $(y+4) = 3/5(x-2)$

Take the denominator 5 to the left side of the equation.

⇒ $5(y+4) = 3(x-2)$

Now, multiply the number outside the bracket to each term inside the bracket.

⇒ $5y+20 = 3x -6$

⇒ $5y = 3x-26$

Divide by 5 on both sides of the equation,

⇒ $y = (3/5)x + 26/5$

Therefore, the equation of the line is  $y = (3/5)x + 26/5$

Answer 2

Answer:

3x - 5y = 26

Step-by-step explanation:

y = mx + c

y = (3/5)x + c

-4 = (3/5)(2) + c

-4 = 6/5 + c

c = -4 - 6/5

c = -26/5

y = (3/5)x - 26/5

Standard form is:

ax + by = c

y = (3/5)x - 26/5

5y = 3x - 26

3x - 5y = 26