We are given a line with a slope of \( m = 4 \) that passes through the point \( \left(\frac{3}{8}, \frac{1}{2}\right) \).
To analyze the statements:
-
The y-intercept is -1.
- To find the y-intercept, we can use the slope-intercept form of the equation: \( y = mx + b \). We know: \[ \frac{1}{2} = 4 \left(\frac{3}{8}\right) + b \] \[ \frac{1}{2} = \frac{3}{2} + b \] \[ b = \frac{1}{2} - \frac{3}{2} = -1 \]
- This statement is true.
-
The slope-intercept equation is \( y = 4x - 1 \).
- From our calculation above, we find: \[ y = 4x - 1 \]
- This statement is true.
-
The point-slope equation is \( y - \frac{3}{8} = 4(x - \frac{1}{2}) \).
- The point-slope form is \( y - y_1 = m(x - x_1) \), where \( (x_1, y_1) = \left(\frac{3}{8}, \frac{1}{2}\right) \). \[ y - \frac{1}{2} = 4\left(x - \frac{3}{8}\right) \]
- The statement given uses the values incorrectly. The correct point-slope form should be: \[ y - \frac{1}{2} = 4\left(x - \frac{3}{8}\right) \]
- This statement is false.
-
The Point \( \left(\frac{3}{8}, \frac{1}{2}\right) \) corresponds to \( (x_1, y_1) \) in the point-slope form of the equation.
- In the point-slope form, \( (x_1, y_1) = \left(\frac{3}{8}, \frac{1}{2}\right) \) is indeed correct since \( y_1 = \frac{1}{2} \) and \( x_1 = \frac{3}{8} \).
- This statement is true.
In summary, the true statements are:
- The y-intercept is -1.
- The slope-intercept equation is \( y = 4x - 1 \).
- The Point \( \left(\frac{3}{8}, \frac{1}{2}\right) \) corresponds to \( (x_1, y_1) \) in the point-slope form of the equation.