Write the point-slope form of the line satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Slope \( =4 \), passing through \( (-7,4) \) Type the point-slope form of the equation of the line. (Simplify your answer. Use integers or fractions for any numbers in the equation.) Type the slope-intercept form of the equation of the line. \( \square \) (Use integers or simplified fractions for any numbers in the equation.) (

The point-slope form of the equation of a line can be written as \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is a point on the line. Substituting the given slope \( m = 4 \) and the point \( (-7, 4) \): \[ y - 4 = 4(x + 7) \] Now, to rewrite this in slope-intercept form \( y = mx + b \), we simplify: \[ y - 4 = 4x + 28 \] \[ y = 4x + 32 \] So, the final forms are: Point-slope: \( y - 4 = 4(x + 7) \) Slope-intercept: \( y = 4x + 32 \) Did you know that point-slope form is particularly useful for quickly sketching lines? Just plug in the slope and a point, and you can easily see how steep the line will be and where it will cross through that point. It's like having a map to your destination! Whenever you're dealing with equations of lines, a common mistake is forgetting to distribute the slope correctly or to be careful with signs. Always double-check your algebra, especially when moving between forms! A small slip can lead to significantly different graphs.