Question

x+y=3 write the slope-intercept form of the equation of the line through the given point with the given slope

Answer 1

To write the equation of a line in slope-intercept form (which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), we first need to derive it from the provided line equation and information about the slope and point.

However, the equation you've given is \( x + y = 3 \). We can manipulate this equation to slope-intercept form first to identify the slope.

### Step 1: Convert to slope-intercept form

Starting from:
\[
x + y = 3
\]

We can isolate \( y \):
\[
y = -x + 3
\]

Here, we can see that the slope \( m \) of the line is \( -1 \).

### Step 2: Write the equation of the line with the given slope and point

If you have a specific slope and point (let's denote this point as \( (x_1, y_1) \)), you can then use the point-slope form of the line, which is:
\[
y - y_1 = m(x - x_1)
\]

### Step 3: Rearranging to slope-intercept form

Once you apply the point-slope form, you can then rearrange it into slope-intercept form.

If you provide the point and the slope that you want to use, I can help you write that specific equation in slope-intercept form!