Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation.
(-7,-2); y=-3x+4
A line parallel to another line will have the same slope. Since we are given 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 can identify the slope of the given line by looking at the coefficient of \( x \). In the given equation \( y = -3x + 4 \), the slope \( m \) is -3.
To find the equation of the line that is parallel to this line and passes through the point (-7, -2), we will keep the same slope and only alter the y-intercept \( b \). Thus, the slope of our new line will also be -3.
The slope-intercept form of the line we are looking for is:
\[ y = mx + b \]
\[ y = -3x + b \]
Next, we need to find the y-intercept \( b \). Since the line passes through the point (-7, -2), we can substitute those coordinates into the equation for \( x \) and \( y \) to solve for \( b \):
\[ -2 = -3(-7) + b \]
\[ -2 = 21 + b \]
Now, subtract 21 from both sides to solve for \( b \):
\[ b = -2 - 21 \]
\[ b = -23 \]
Now that we have the y-intercept, we can write the final equation of the line:
\[ y = -3x - 23 \]
This is the equation in slope-intercept form of the line that is parallel to \( y = -3x + 4 \) and passes through the point (-7, -2).