Final answer:
To convert the equation 6x + 2y = -4 into slope-intercept form, we rearrange the equation to isolate y and get y = -3x - 2. The equation of a line passing through two points is y = mx + b, where m is the slope and b is the y-intercept. If we know the slope m and the y-intercept b, we can directly write the equation in slope-intercept form as y = mx + b.
Step-by-step explanation:
The standard form of a linear equation is given by ax + by = c, where a, b, and c are constants. To convert the equation 6x + 2y = -4 into slope-intercept form, we need to isolate y on one side of the equation. Rearranging the equation, we get 2y = -6x - 4. Dividing both sides by 2, we obtain y = -3x - 2. Therefore, the equation in slope-intercept form is y = -3x - 2.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. If we have two points that the graph passes through, we can use the slope formula to find the slope and substitute one of the points into the equation to find the y-intercept. For example, if the graph passes through the points (x1, y1) and (x2, y2), the slope is given by m = (y2 - y1) / (x2 - x1). Using this slope and one of the points, we can substitute it into the equation y = mx + b to find b. Therefore, the equation of the line passing through two points is y = mx + b.
Finally, if we know the slope m and the y-intercept b, we can directly write the equation in slope-intercept form as y = mx + b. For example, if the slope is 3 and the y-intercept is 2, the equation would be y = 3x + 2.