Write the slope-intercept form of the equation of the line satisfying the given conditions.
Through (−6,12); slope −7/12
To find the slope-intercept form of the equation of the line, we need the slope and a point on the line. We are given that the slope is -7/12 and the point (-6, 12).
The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
To find the equation, we can plug in the given values into the slope-intercept form:
y = (-7/12)x + b
To determine the value of b, we can use the given point (-6,12). Substitute x = -6 and y = 12 into the equation:
12 = (-7/12)(-6) + b
Simplifying:
12 = 7/2 + b
Multiply both sides by 2 to get rid of the fraction:
24 = 7 + 2b
Subtract 7 from both sides:
17 = 2b
Divide both sides by 2:
b = 17/2
Now, we have the value of b. Substituting it back into the equation, we get the final equation:
y = (-7/12)x + 17/2
The slope-intercept form of the equation of a line is given by y = mx + b, where m represents the slope and b represents the y-intercept.
Given that the slope is -7/12 and the line passes through (-6, 12), we can substitute these values into the equation.
Let's solve for b, the y-intercept.
y = mx + b
12 = (-7/12) * (-6) + b
12 = 7/2 + b
To solve for b, subtract 7/2 from both sides:
12 - 7/2 = b
Multiplying 12 by 2/2, we get a common denominator:
24/2 - 7/2 = b
24 - 7/2 = b
Now, find a common denominator:
24/2 - 7/2 = b
Combine the fractions:
17/2 = b
The y-intercept, b, is equal to 17/2. Now, we can write the equation of the line:
y = (-7/12)x + 17/2
Therefore, the slope-intercept form of the equation of the line is y = (-7/12)x + 17/2.
To find the slope-intercept form of the equation of a line, we use the formula: y = mx + b, where m represents the slope of the line and b represents the y-intercept.
Given that the slope (m) is -7/12 and the point (-6, 12) lies on this line, we can use the point-slope form of the equation: y - y1 = m(x - x1), where (x1, y1) is the given point.
Substituting the values, we have:
y - 12 = (-7/12)(x - (-6))
Simplifying further, we get:
y - 12 = (-7/12)(x + 6)
To convert this equation into slope-intercept form (y = mx + b), we need to isolate y. Let's continue simplifying:
y - 12 = (-7/12)(x + 6)
y - 12 = (-7/12)x - 7/2
Adding 12 to both sides to isolate y, we have:
y = (-7/12)x - 7/2 + 12
Combining the constants, 7/2 and 12, we get 7/2 + 24/2 = 31/2:
y = (-7/12)x + 31/2
Therefore, the slope-intercept form of the equation of the line satisfying the given conditions is y = (-7/12)x + 31/2.