Final answer:
To find the value of b in the slope-intercept form of the equation parallel to y = 3x + 5 and passing through the point (–1, −2), we use the fact that parallel lines have the same slope. The equation of the line is y = 3x + 1.
Step-by-step explanation:
To find the value of b in the slope-intercept form of the equation, which is parallel to y = 3x + 5 and passes through the point (–1, −2), we need to use the fact that parallel lines have the same slope.
So, the slope of the equation we are looking for is also 3.
We can use the point-slope form of the equation y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.
Substituting the values, we get y - (-2) = 3(x - (-1)).
Simplifying further, we have y + 2 = 3(x + 1).
Finally, we can convert the equation to slope-intercept form by isolating y. We get y = 3x + 1.
Therefore, the value of b is 1.
Learn more about Slope-intercept form of equations