Give the equation of the line passing through the point
( − 9 , − 37 ) that is parallel to
y

To find the equation of a line that is parallel to the line $y = 4x + 5$ and passes through the point $(-9, -37)$, follow these steps:

1. Identify the Slope of the Given Line:

The equation given is in slope-intercept form $y = mx + b$, where $m$ is the slope. For the line $y = 4x + 5$, the slope $m$ is 4.

2. Use the Point-Slope Form:

The point-slope form of a line's equation is: $y - y_1 = m(x - x_1)$ where $m$ is the slope and $(x_1, y_1)$ is a point on the line.

Substitute $m = 4$, $x_1 = -9$, and $y_1 = -37$ into the point-slope form: $y - (-37) = 4(x - (-9))$ $y + 37 = 4(x + 9)$

3. Simplify to Slope-Intercept Form:

Now, simplify the equation to get it in slope-intercept form $y = mx + b$: $y + 37 = 4x + 36$ $y = 4x + 36 - 37$ $y = 4x - 1$

Final Answer:

The equation of the line in slope-intercept form is: $\boxed{y = 4x - 1}$

Would you like more details on any of these steps?

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Here are some related questions you might find interesting:

1. How do you find the equation of a line given two points?
2. What does it mean for two lines to be parallel?
3. How do you convert from point-slope form to standard form?
4. How do you find the equation of a line perpendicular to a given line?
5. What is the relationship between the slopes of parallel lines?

Tip: When two lines are parallel, their slopes are equal. This is key to solving many problems involving parallel lines.