Find the equation of the line with a slope of \( m=8 \) that passes through the point \( (4,2) \). Write the equation in both the point-slope form and the slope-intercept form. point-slope: slope-intercept:
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Using the point-slope form, the equation of the line can be written as \( y - y_1 = m(x - x_1) \). Plugging in the point \( (4, 2) \) and the slope \( m=8 \), we get: **Point-slope:** \( y - 2 = 8(x - 4) \). Now, to convert this into slope-intercept form, we simply solve for \( y \): **Slope-intercept:** \( y = 8x - 30 \). So there you have it! A line that steeply climbs with a slope of 8, starting from that cozy point (4,2). Happy graphing!
