What is the equation of the line in slope-intercept form that passes through point (1, –2) and is parallel to the line y = 3x – 2? Show all necessary steps.

Answer 1

To find the equation of the line that passes through the point (1, –2) and is parallel to the line given by the equation $y=3x-2$, we can follow these steps:

1. Identify the Slope: The slope of the line $y=3x-2$ is 3 (since it is in the form $y=mx+b$, where $m$ is the slope). Since parallel lines have the same slope, the slope of our new line will also be 3.

2. Use the Point-Slope Form: We can use the point-slope form of the equation of a line, which is given by: $$y-y_1=m(x-x_1)$$ where $(x_1,y_1)$ is the point the line passes through and $m$ is the slope. Here, $(x_1,y_1)=(1,-2)$ and $m=3$.

3. Substitute the Values: Plugging the values into the point-slope form: $$y-(-2)=3(x-1)$$ Simplifying this, we get: $$y+2=3(x-1)$$

4. Distribute the Slope: $$y+2=3x-3$$

5. Isolate y: Now, we need to solve for $y$: $$y=3x-3-2$$ $$y=3x-5$$

Thus, the equation of the line in slope-intercept form that passes through the point (1, –2) and is parallel to the line $y=3x-2$ is: $$\boxed{{\displaystyle y=3x-5}}$$