What is an equation of the line that passes through the point (5,8) and is parallel to the line x + y = 8?
Parallel lines have equal slopes. Get the equation, x + y = 8, in slopeintercept form to identify the slope.
Slopeintercept form is y = mx + b m is the slope b is the yintercept x + y = 8 y = x + 8 {subtracted x from each side} slope = 1 {the coefficient of x} Use the slope of 1 and the point (5,8) to get the equation of the new line. Use slopeintercept form and substitute 5 in for x, 8 in for y, and 1 in for m, to find the yintercept. y = mx + b {slopeintercept form} 8 = 1(5) + b {substituted} 8 = 5 + b {multiplied} b = 3 {subtracted 5 from each side} yintercept is 3 The slope is 1 and the yintercept is 3. Substitute back into slopeintercept form to get the equation of the line. y = x + 3 {substituted} Check with graphing calculator:
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