Question
The straight line y = mx -4 passes through the point (4, 16) calculate the gradient of the line
Answers
GPT-4o mini
To determine the gradient \( m \) of the line represented by the equation \( y = mx - 4 \) that also passes through the point \( (4, 16) \), we can substitute the coordinates of the point into the equation and solve for \( m \).
Given the point \( (x, y) = (4, 16) \):
1. Substitute \( x = 4 \) and \( y = 16 \) into the equation:
\[
16 = m(4) - 4
\]
2. Simplify the equation:
\[
16 = 4m - 4
\]
3. Add 4 to both sides to isolate the term with \( m \):
\[
20 = 4m
\]
4. Now, divide both sides by 4 to solve for \( m \):
\[
m = \frac{20}{4} = 5
\]
Thus, the gradient of the line is \( \boxed{5} \).
Given the point \( (x, y) = (4, 16) \):
1. Substitute \( x = 4 \) and \( y = 16 \) into the equation:
\[
16 = m(4) - 4
\]
2. Simplify the equation:
\[
16 = 4m - 4
\]
3. Add 4 to both sides to isolate the term with \( m \):
\[
20 = 4m
\]
4. Now, divide both sides by 4 to solve for \( m \):
\[
m = \frac{20}{4} = 5
\]
Thus, the gradient of the line is \( \boxed{5} \).