To find the equation of a line given its slope and a point it passes through, we'll use the slope-intercept form of the equation of a line, which is:
[tex]\[ y = mx + b \][/tex]
Here, [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
1. Identify the given values:
- The slope ([tex]\( m \)[/tex]) is -7.
- The line passes through the point (1, 9). This means [tex]\( x_1 = 1 \)[/tex] and [tex]\( y_1 = 9 \)[/tex].
2. Substitute the given point and slope into the slope-intercept form to find [tex]\( b \)[/tex]:
We use the point (1, 9) to find the y-intercept [tex]\( b \)[/tex]:
Substitute [tex]\( x_1 = 1 \)[/tex], [tex]\( y_1 = 9 \)[/tex], and [tex]\( m = -7 \)[/tex] into the equation:
[tex]\[ y_1 = mx_1 + b \][/tex]
[tex]\[ 9 = -7(1) + b \][/tex]
3. Solve for [tex]\( b \)[/tex]:
[tex]\[ 9 = -7 + b \][/tex]
[tex]\[ 9 + 7 = b \][/tex]
[tex]\[ b = 16 \][/tex]
4. Write the final equation:
Substitute [tex]\( m = -7 \)[/tex] and [tex]\( b = 16 \)[/tex] back into the slope-intercept form:
[tex]\[ y = -7x + 16 \][/tex]
Therefore, the equation of the line with a slope of -7 that passes through the point (1, 9) is:
[tex]\[
y = -7x + 16
\][/tex]
