Line1 goes through (1,3) and is perpendicular to Line2. Line2 goes through (4,2) and (-1,1) Find: a: m1=_____b: the equation for line 1 in slope-intercept form=________. Graph and label both lines.

⚑ Flag

To approach this problem, we need to find the linear equations for both the lines. Note that line 1 is perpendicular to line 2. This means that the slope of line 1 is the negative reciprocal of the slope of line 2 and vice versa. This means that if we find the slope of line 2, we can easily compute the slope of line 1!To find the slope of line 2, use the equation:        y2 - y1m = ---------        x2 - x1where (x1, y1) represents one point on the line and (x2, y2) represents another point on the lineWhen we plug the values in, we find that the slope of line 2 is m = 1. The negative reciprocal of 1 is -1, and so is the slope of line 1!Now we need to write the equation for line 1 in slope-intercept form. Slope intercept form is the following:y = mx+bwhere m = slope and b = y-interceptWe already have the slope of line 1, which is -1. To find the y-intercept, we set the equation equal to b (b = y - mx) and plug in a point. b = (0,4), and so the equation is y = -x+4.