Question

Put the following equation of a line into slope-intercept form, simplifying all fractions:

6x+2y=−10.
a) y=−3x−5
b) y=−3x+5
c) y=−2x+10
d) y=−2x−10

Answer 1

The equation 6x+2y=−10 is converted to slope-intercept form by dividing all terms by 2 and then isolating y to get y=−3x−5, matching option (a).

Step-by-step explanation:

To convert the given equation of a line 6x+2y=−10 into slope-intercept form, we need to isolate the y-variable on one side of the equation. We will simplify all fractions to find the slope and the y-intercept of the line. The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Here are the steps to convert the equation:

1. Divide every term by 2 to simplify and isolate y: 6x/2 + 2y/2 = −10/2, which simplifies to 3x + y = −5
2. Subtract 3x from both sides to solve for y: y = −3x − 5

The final slope-intercept form of the equation is y = −3x − 5, which corresponds to option (a).