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 \( =8 \), passing through \( (-2,6) \)

To write the point-slope form, we use the formula \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is the point the line passes through. With a slope of 8 and the point \((-2, 6)\), the equation becomes: \[ y - 6 = 8(x + 2) \] Now, to convert to slope-intercept form, we simplify: \[ y - 6 = 8x + 16 \] \[ y = 8x + 22 \] So the slope-intercept form of the equation is \( y = 8x + 22 \). To visualize the equation, graphing can make it clear how changes in the slope and intercept affect the line. Remember that the slope indicates steepness—this means for every unit you move to the right, you'd move 8 units up! It creates an exciting challenge for sketching your lines. If ever you find yourself grappling with equations, double-check those sign errors! It's quite common to mistakenly flip a sign when transposing numbers or when multiplying during simplifications. Keeping a close eye on your arithmetic can make all the difference!