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Find an equation of the line having the given slope and containing the given point.

[tex]\[ m = -7, \ (1, 9) \][/tex]

Sagot :

GinnyAnsweridn
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]
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