through: (-3,-2), slope = 1

Answer 1

To write the equation of a line given a point and a slope, you can use the point-slope form of the equation of a line, which is:

$$y-y_1=m(x-x_1)$$

where $(x_1,y_1)$ is the point on the line and $m$ is the slope.

For the point $(-3,-2)$ and the slope $1$:

• $x_1=-3$
• $y_1=-2$
• $m=1$

Substituting these values into the point-slope equation:

$$y-(-2)=1(x-(-3))$$

This simplifies to:

$$y+2=1(x+3)$$

Now, distribute the slope:

$$y+2=x+3$$

Subtract $2$ from both sides to put it into slope-intercept form:

$$y=x+3-2$$ $$y=x+1$$

So, the equation of the line through the point $(-3,-2)$ with slope $1$ is:

$$y=x+1$$