What is an equation of the line through (0 –3) with slope 2/5. (A)-5x+2y=15 (B)-5x-2y=-15 (C)2x-5y=15 (D)-2x+5y=15

Answer 1

There are three ways to write the equation of a line: slope intercept form, point slope form, and standard (general) form.

Slope-intercept form: y = mx + b

Here, m is the slope of the line (Δy / Δx) and b is the y-intercept.

Point-slope form: (y − y₁) = m(x − x₁)

Here, y₁ is the y-coordinate of your chosen point and x₁ is the x-coordinate of your point.

Standard form: Ax + By = C

Here, A, B, and C are integers.

From the looks of this question, you are supposed to write the equation for this point and slope in standard form. You can find this equation by rewriting the equation in point-slope form so that it fits the formula for standard form.

m = 2/5

(x₁, y₁) = (0,-3)

(y - [-3]) = 2/5(x - 0)

(y + 3) = 2/5x

y = 2/5x - 3

Multiply both sides by 5 to eliminate the fraction.

5y = 2x - 15

Subtract 2x from both sides.

-2x + 5y = -15

Multiply both sides of the equation by -1.

2x - 5y = 15

Check your answer by plugging in your point.

2(0) - 5(-3) = 15

- (-15) = 15

15 = 15