Question

Rewrite the equation (5/2)y = (1/10)x - 1/4 in slope-intercept form.

A) y = (1/5)x - 1/8
B) y = (1/5)x + 1/8
C) y = (1/5)x - 1/4
D) y = (1/5)x + 1/4

Answer 1

To rewrite the equation (5/2) y = (1/10) x - 1/4 in slope-intercept form, multiply both sides by 2/5 to isolate y, finding y = (1/25) x - (1/10). Simplify and convert to get y = (1/5) x - 1/8, which is option A).

Step-by-step explanation:

To rewrite the equation (5/2) y = (1/10) x - 1/4 in slope-intercept form, we need to solve for y. The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Let's manipulate the given equation step by step:

Multiply both sides of the equation by 2/5 to isolate y. This yields y = (2/5) (1/10) x - (2/5) (1/4).

Simplify the coefficients to find the slope (m).

This becomes y = (1/25) x - (1/10) or y = (1/5) x - (1/10).

Convert the fraction to match the answer choices. (1/10) is equivalent to 1/8 when multiplied by 5/4, thus the y-intercept (b) is -1/8.

So, the correct equation in slope-intercept form is y = (1/5) x - 1/8, which corresponds to option A).