To find the gradient (slope) and y-intercept for each of the provided equations, we can analyze each one individually:
-
Equation: \( Y = x + 2 \)
- Gradient (slope): The coefficient of \( x \) is \( 1 \).
- Y-intercept: This is the value of \( Y \) when \( x = 0 \). Substituting \( x = 0 \) gives \( Y = 2 \).
- Gradient = 1, Y-intercept = 2
-
Equation: \( Y = 3x \)
- Gradient (slope): The coefficient of \( x \) is \( 3 \).
- Y-intercept: Substituting \( x = 0 \) gives \( Y = 0 \).
- Gradient = 3, Y-intercept = 0
-
Equation: \( 2x + 5y = 10 \)
- To find the gradient and y-intercept, we can rearrange this into the slope-intercept form \( Y = mx + b \): \[ 5y = -2x + 10 \ y = -\frac{2}{5}x + 2 \]
- Gradient (slope): The coefficient of \( x \) is \( -\frac{2}{5} \).
- Y-intercept: This is the value when \( x = 0 \), giving \( Y = 2 \).
- Gradient = -\frac{2}{5}, Y-intercept = 2
-
Equation: \( Y = 3 \)
- This is a horizontal line.
- Gradient (slope): The slope is \( 0 \) because there is no change in \( Y \) as \( X \) changes.
- Y-intercept: This is the value of \( Y \) which is \( 3 \).
- Gradient = 0, Y-intercept = 3
-
Equation: \( X = 4 \)
- This is a vertical line.
- Gradient (slope): The slope is undefined because the value of \( X \) does not change as \( Y \) changes.
- Y-intercept: Since this line does not cross the \( Y \)-axis, it does not have a y-intercept.
- Gradient = undefined, Y-intercept = None
Summary:
- \(Y = x + 2\): Gradient = 1, Y-intercept = 2
- \(Y = 3x\): Gradient = 3, Y-intercept = 0
- \(2x + 5y = 10\): Gradient = -\(\frac{2}{5}\), Y-intercept = 2
- \(Y = 3\): Gradient = 0, Y-intercept = 3
- \(X = 4\): Gradient = undefined, Y-intercept = None
1 answer