Final answer:
To convert the equation 3x - 2y + 10 = 0 to slope-intercept form, isolate y by subtracting 3x from both sides and dividing by -2, resulting in y = (3/2)x + 5, where 3/2 is the slope and 5 is the y-intercept.
Step-by-step explanation:
To find the equation 3x − 2y + 10 = 0 in slope-intercept form, we need to solve for y in terms of x. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. By following steps to rearrange the given equation, we can identify these parameters.
First, let's isolate y on one side of the equation:
- Start by subtracting 3x from both sides of the equation to get − 2y = − 3x − 10.
- Next, divide every term by − 2 to solve for y, resulting in y = (3/2)x + 5.
In the equation y = (3/2)x + 5, the slope (m) is 3/2, and the y-intercept (b) is 5. The slope tells us for every increase of 1 on the x-axis, the y-value will rise by 3/2 and the y-intercept is the point where the line crosses the y-axis.